During his closing argument in the 2004 murder trial of Brenda Andrew in Oklahoma, a prosecutor dangled her thong underwear before the jury. She had packed the undergarment for a trip to Mexico a few days after her estranged husband was killed.

The prosecutor, Gayland Gieger, said the item was strong evidence that Ms. Andrew had murdered her husband. “The grieving widow packs this to run off with her boyfriend,” he said, holding her underwear.

“That’s enough,” he said. “Can’t twist the facts, folks. Can’t twist the evidence.”

The spectacle “drew gasps from the crowded courtroom,” a local newspaper reported. The jury convicted Ms. Andrew and condemned her to death. She is the only woman on the state’s death row.

Later this month, the Supreme Court will consider whether to hear Ms. Andrew’s appeal, which said the display of her underwear was a representative part of an unrelenting strategy by prosecutors, as a dissenting judge put it, “of introducing evidence that has no purpose other than to hammer home that Brenda Andrew is a bad wife, a bad mother and a bad woman.”

Nathalie Greenfield, one of Ms. Andrew’s lawyers, said gender stereotypes infected the trial and poisoned the jury.

“Every single day the state was presenting gendered evidence about her appearance, about her clothing, about her sexual practices, about her skills as a mother,” she said. “We’ve got someone who is at risk of execution for not conforming to gender stereotypes.”

A brief supporting Ms. Andrew from a former federal judge and others said the volume of prejudicial evidence portraying her as “a hypersexual seductress” warranted review. “The prosecution introduced reams of inflammatory evidence about Ms. Andrew’s sexuality,” the brief said, including “lurid details of her multiple affairs, her suggestive clothing and lingerie, her cleavage and even a book on how to ‘Drive a Man Wild in Bed.’”

The Supreme Court has overturned a death sentence based on testimony tainted by racial bias, saying that “some toxins can be deadly in small doses.” Ms. Andrew’s case asks whether courts should take a similar approach to evidence grounded in gender stereotypes.

“Gender bias is normalized and tolerated to an extent that racial bias no longer is in the administration of the death penalty,” said Sandra Babcock, a law professor at Cornell who represents Ms. Andrew in a related case. “Women on trial for capital murder have been subjected to similar shaming tactics for hundreds of years.”

In urging the Supreme Court not to hear the case, Andrew v. White, No. 23-6573, prosecutors said almost nothing to justify using evidence about Ms. Andrew’s appearance and sexuality. They argued instead that it was “but a drop in the ocean” in the case against her. State and federal appeals courts have more or less agreed, suggesting that the prosecutors’ presentation was regrettable but that there was ample evidence of Ms. Andrew’s guilt.

The Oklahoma Court of Criminal Appeals, for instance, said in 2007 that it was “struggling to find any relevance” for much of the contested evidence but added that “even so, the introduction of this evidence was harmless.”

The U.S. Court of Appeals for the 10th Circuit said last year that it shared the state court’s “concerns about some of the ‘sexual and sexualizing’ evidence admitted at trial” but that Ms. Andrew could not overcome the high hurdles to challenging a state-court conviction in federal court.

Ms. Andrew’s boyfriend, James Pavatt, admitted to shooting her husband and said he had acted alone. But there was reason to think Ms. Andrew was involved, as part of a plot to obtain the proceeds of a life insurance policy, and the authorities charged both of them with capital murder. Mr. Pavatt was also sentenced to death, and he is scheduled to be executed in July.

In a partial dissent from the state court’s ruling in 2007, Judge Arlene Johnson, the only woman on the court at the time, said she would have let Ms. Andrew’s conviction stand. But, she wrote, “I find it impossible to say with confidence that the death penalty here was not imposed as a consequence of improper evidence and argument” that served “to trivialize the value of her life in the minds of the jurors.”

In dissent last year from the 10th Circuit’s decision, Judge Robert E. Bacharach went further, saying he would have overturned not only her death sentence but also her conviction.

“The state focused from start to finish on Ms. Andrew’s sex life,” Judge Bacharach wrote. “This focus portrayed Ms. Andrew as a scarlet woman, a modern Jezebel, sparking distrust based on her loose morals. The drumbeat on Ms. Andrew’s sex life continued in closing argument, plucking away any realistic chance that the jury would seriously consider her version of events.”

Ms. Babcock said a male defendant would not have been treated as Ms. Andrew had been. “It’s inconceivable that the prosecution would dangle his favorite pair of boxers in front of the jury,” she said, “and argue that they proved his guilt.”