Plaintiff-Appellant Independent Coca-Cola Employees’ Union of Lake Charles, *138No. 1060 (“the Union”) appeals the district court’s grant of summary judgment in favor of Defendant-Appellee Coca-Cola Bottling Company United, Inc. (“Coca-Cola”). The district court ruled that the Union’s cause of action to compel Coca-Cola to arbitrate had prescribed (“time-barred”) because Coca-Cola informed the Union of its unequivocal refusal to arbitrate on November 27, 2002, thereby triggering the six-month statute of limitations under Section 301(a) of the Labor Management Relations Act (“LMRA”), 29 U.S.C. § 185(a), yet the Union did not sue Coca-Cola until June 2, 2003. We affirm.
I. FACTS AND PROCEEDINGS
In August 1994, Coca-Cola suspended Arthur Etienne, its employee and a member of the Union, pending an investigation of his arrest. A collective bargaining agreement (“CBA”) between Coca-Cola and the Union contains a grievance and arbitration procedure which is the exclusive means by which aggrieved employees may settle disputes with their employer. The Union filed a grievance contesting Etienne’s suspension. (In May 1996, Coca-Cola reinstated Etienne after the criminal charges were dismissed.)
In August 1998, Coca-Cola terminated Etienne for “inefficiency, incompetency, neglect of work or decective [sic] workmanship.” In September 1998, Etienne and the Union filed another grievance with Coca-Cola, this one contesting Etienne’s termination. Coca-Cola denied the grievance in December, and, in February 1999, the Union notified Coca-Cola of its and Etienne’s intent to arbitrate the dispute under the CBA. Coca-Cola, through its counsel, filed a written request with the Federal Mediation and Conciliation Service (“FMCS”) to provide an arbitration panel. In March 1999, the FMCS submitted an arbitration panel.
Although the arbitration panel remained available, the parties postponed selection of an arbitrator while they pursued amicable settlement of Etienne’s grievance. The Union contends that Coca-Cola’s request for an arbitration panel and its continual negotiations to resolve Etienne’s grievance led the Union to believe that Coca-Cola had formally requested, acknowledged, and accepted arbitration of Etienne’s grievance. The Union also asserts that it understood that the parties would submit the dispute to arbitration in the event that settlement negotiations were unsuccessful.
In March 2002, counsel for Coca-Cola wrote to Ken Schexnayder, a Union representative and spokesman, advising the Union that, although Coca-Cola had no legal obligation to Etienne, it would settle the grievance for $12,000. In its letter, Coca-Cola informed the Union that the offer would remain open for thirty days. (There is no evidence in the record that the Union or Etienne accepted the settlement offer, counter-offered, or otherwise responded within 30 days.)
On November 19, 2002, the Union responded to Coca-Cola’s offer by letter in which it outlined its position. The Union informed Coca-Cola that “[i]t is our position that this grievance is deemed granted and that Coca-Cola is foreclosed from contesting this grievance because of its failure to adhere to the time limitations set forth in the grievance procedure.”3
*139On November 27, 2002, Coca-Cola responded to the Union’s November 19 letter. Coca-Cola informed the Union and Etienne that any cause of action that they may have had had prescribed in six months. Coca-Cola’s letter stated:
Please be advised that we totally disagree with the factual and legal conclusions set forth in your letter of November 19, 2002.
We have on numerous occasions tried to amicably settle any grievance Mr. Etienne may have had.
As you are aware, under La. Civil Code Art. 3494, a claim for wages or compensation is prescribed after three (3) years. Additionally, any cause of action the Union or Mr. Etienne may have had prescribed in six (6) months. (Del Costello v. International Brotherhood of Teamsters, 462 U.S. 151, 103 S.Ct. 2281, 76 L.Ed.2d 476; and Sussman v. News-Journal Corp., 742 F.2d 1466).
We are of the opinion that neither the Union nor Mr. Etienne have a viable cause of action at this time.
On December 4, 2002, the Union and Etienne responded to Coca-Cola’s November 27 letter. They informed Coca-Cola that any dispute over whether they had a viable cause of action was not ripe because the parties had not exhausted the grievance and arbitration procedure. They also asked Coca-Cola to provide them with dates on which the parties could meet to select an arbitrator.
On December 11, Coca-Cola responded to the Union, stating:
Please be advised that any cause of action to compel arbitration has prescribed. By letter dated March 14, 2002, the Union was advised that the Company had no legal obligation to Mr. Etienne, and the offer to settle the grievance would expire in 30 days from the date of that letter.
Consequently, the Company is of the opinion it has no legal or contractual obligation to arbitrate Mr. Etienne’s grievance at this time.
On June 2, 2003, the Union sued Coca-Cola in the United States District Court for the Western District of Louisiana under Section 301(a) of the LMRA4 to compel Coca-Cola to arbitrate the Etienne grievance. In October 2003, Coca-Cola filed a motion for summary judgment, maintaining that the Union’s cause of action to compel arbitration was time-barred. The district court found that in its November 27, 2002 letter, Coca-Cola had clearly and unequivocally refused to arbitrate Etienne’s grievance. As more than six months had passed between Coca-Cola’s November 27 letter and the filing of the Union’s suit, the district court concluded that the plaintiffs were time-barred from seeking to compel arbitration and granted Coca-Cola’s motion for summary judgment, dismissing the action with prejudice.
The Union then filed a Motion to Alter or Amend Judgment under Federal Rule of Civil Procedure 59. In its motion, the Union argued that the November 27 letter constituted constructive notice only of Coca-Cola’s refusal to arbitrate. The district court disagreed, concluding that the Union was merely attempting to re-litigate Coca-Cola’s motion for summary judgment. The district court denied the motion to alter or amend. The Union timely filed its notice of appeal.
II. ANALYSIS
A. Summary Judgment
1. Standard of Review
We review a district court’s grant of summary judgment de novo, using the same standard as that applied by the dis*140trict court.5 Summary judgment is “proper, if, viewing the evidence and inferences drawn from that evidence in the light most favorable to the non-moving party, there is no genuine issue of material fact and the moving part is entitled to judgment as a matter of law.”6 At this stage, “a court may not weigh the evidence or evaluate the credibility of witnesses, and all justifiable inferences will be made in the non-moving party’s favor.”7
2. Applicable Law
We have held that “an action on a collective bargaining agreement under section 301 of the Labor Management Relations Act is governed by the six-month limitation included in section 10(b) of the National Labor Relations Act.”8 The six-month limitation period “accrues when one party clearly refuses to arbitrate the dispute.” 9 To “make it clear” that an employer refuses to arbitrate, circuit courts have held that one of the parties must take the unequivocal position that it will not arbitrate.10 Whether the employer has unequivocally refused to arbitrate turns on the particular facts of each case.11
*141The Union argues that Coca-Cola did not unequivocally refuse to arbitrate before sending its December 11, 2002 letter to the Union. Coca-Cola counters that it unequivocally refused to arbitrate in its November 27, 2002 letter. We discern no error in the district court’s determination that Coca-Cola’s November 27 letter constituted an unequivocal refusal to arbitrate.
In that letter, Coca-Cola informed the Union that any cause of action that it or Etienne may have had was prescribed. Coca-Cola made clear its position that neither the Union nor Etienne had a “viable cause of action” at that time because any cause of action had prescribed. We agree with the district court that when one party tells another that it has no viable cause of action because any claims that it might have had are now time-barred, that party has unequivocally refused to arbitrate. Although Coca-Cola might have chosen its words more carefully, there is no need for a party refusing to arbitrate to use that term (or any other talismanic words) to express its refusal to arbitrate.12 Further, there is no record evidence that Coca-Cola engaged in any activity subsequent to the November 27 letter that would contradict *142its position as expressed therein.13 We perceive no doubt or equivocation in Coca-Cola’s position that it did not intend to arbitrate claims that the Union and Etienne could no longer pursue by virtue of the statute of limitations.
The Union relies heavily on AAA Plumbing Pottery Corp. to support its proposition that Coca-Cola’s November letter should not constitute an unequivocal refusal to arbitrate.14 AAA Plumbing is distinguishable on the facts. There, the employer stated that “ ‘I’m sure you will agree that the matter is closed and it would be inappropriate to reopen it at this time.’ ”15 The Eleventh Circuit found this language equivocal in that it was no more than “an attempt to persuade the [unionj’s counsel that [its client] had no basis for the suggestion that the parties should return to arbitration.”16 Here, in contrast, the declaration in Coca-Cola’s letter that the Union’s and Etienne’s claim had prescribed is not merely suggestive of Coca-Cola’s rejection of arbitration but an unambiguous and unequivocal statement of its position that there was no reason to arbitrate a prescribed claim.
As a further distinction, we note that later conduct of the employer in AAA Plumbing contributed to the Eleventh Circuit’s determination that the language in the employer’s letter did not constitute an unequivocal refusal to arbitrate. There, the lawyer for the employer sent a subsequent letter to opposing counsel in which he stated that he “would be interested to see what the Union’s position [was] concerning [the employee’s] backpay.”17 In contrast, there is no record evidence that Coca-Cola engaged in any conduct subsequent to its November 27 letter that could be seen as casting doubt on its stated position that the Union’s and Etienne’s causes of action had prescribed. That Coca-Cola might have engaged in intermittent negotiations during the course of approximately three years over Etienne’s grievance before sending the November letter is of no moment: Once Coca-Cola sent that letter to the Union, Coca-Cola’s position that it would not arbitrate a time-barred claim was unmistakable.18 We agree with the district court’s ruling that Coca-Cola’s November 27, 2002 letter constituted an unequivocal refusal to arbitrate and, consequently, that the Union’s claim prescribed before it filed suit against Coca-Cola on June 2, 2003.
*143B. Motion to Alter or Amend
1. Standard of Review
We generally review the denial of a motion to alter or to amend judgment under Rule 59(e) for abuse of discretion.19 If the district court’s ruling implicates reconsideration of a question of law, we review the denial de novo.20
2. Analysis
A Rule 59(e) motion to alter or to amend judgment “ ‘calls into question the correctness of a judgment.’ ”21 We have previously held that a Rule 59(e) motion “is not the proper vehicle for rehashing evidence, legal theories, or arguments that could have been offered or raised before the entry of judgment.”22 A Rule 59(e) motion “ ‘serve[s] the narrow purpose of allowing a party to correct manifest errors of law or fact or to present newly discovered evidence.’ ”23 Rule 59(e) also provides relief to a party when there has been an intervening change in the controlling law.24 Relief under Rule 59(e) is an extraordinary remedy that should be used sparingly.25
In its motion to alter or amend judgment in the district court, the Union insisted that Coca-Cola’s November 27, 2002 letter was at best constructive notice of its refusal to arbitrate. In paragraph eight of its Statement of Material Facts as to Which There is no Genuine Issue to be Tried, Coca-Cola wrote:
The Union and Arthur Etienne received constructive notice of the letter sent by G. Michael Pharis to Marshall J. Simien, Jr. dated November 27, 2002.
The Union contends that this constitutes a “judicial admission” by Coca-Cola that its November letter constituted constructive notice only, and thus does not entitle Coca-Cola to summary judgment here. To support this proposition, the Union cites to other circuit courts that have held that constructive notice of the refusal to arbitrate is insufficient because the refusal must be unequivocal.26
The Union did not raise this argument in its opposition to Coca-Cola’s motion for summary judgment. Rather, the Union did so for the first time in its motion to alter or to amend judgment before the district court. “Defenses not raised or argued at trial are ordinarily waived by the parties failing to raise them.”27 A Rule 59(e) motion “cannot be used to ar*144gue a case under a new legal theory.”28 The Union could have raised this argument in its Memorandum in Opposition to Coca-Cola’s Motion for Summary Judgment (or even in a supplemental memorandum). Accordingly, we conclude that the Union waived this argument.29 The district court did not abuse its discretion when it denied the motion to alter or to amend.
III. CONCLUSION
For the foregoing reasons, the rulings of the district court are, in all respects,
AFFIRMED.