“We were hopeful their sending it back would mean something,” Mr. Schneider said.

But his hope flagged in March when, he said, two Harris County state district judges virtually rubber-stamped Dr. George Denkowski’s findings in the cases of Mr. Matamoros and a fellow death row inmate, Steven Butler. Dr. Denkowski, the psychologist who testified in the cases of 14 current Texas death row inmates that the convicted men were mentally fit for execution, was reprimanded last year after other psychologists and defense lawyers filed a complaint alleging that he had used discredited evaluation methods.

Lawyers for Mr. Matamoros and Mr. Butler, who have filed objections with the Texas Court of Criminal Appeals, say any findings by Dr. Denkowski should be disregarded. They said that the trial court judges — who are husband and wife — simply adopted Dr. Denkowski’s conclusions instead of examining reams of evidence from other psychologists that they said proved their clients were mentally retarded and ineligible for the death penalty.

“This is a perfect example of the state taking science and trying to prostitute it,” Mr. Schneider said, adding, “The role of the courts is to protect us from junk science.”

Judge Marc Brown, of Harris County District Court, who reviewed the Matamoros case, was in trial and did not respond to a request for comment. His wife, Judge Susan Brown, declined to comment on the Butler case because it is continuing. Calls to Dr. Denkowski were not returned.

But Roe Wilson, Harris County assistant district attorney, contended that the judges had disregarded Dr. Denkowski’s findings.

The judge’s findings in Mr. Butler’s case repeatedly refer to Dr. Denkowski’s findings, but Ms. Wilson said the references were “historical.”

“There was no consideration given and no mention given,” Ms. Wilson said.

The Supreme Court of the United States ruled in 2002 that states could not execute people who were mentally retarded. The court allowed states to decide on guidelines for determining whether a person was mentally retarded. Texas courts have adopted a three-part definition that requires the convicted inmate to have below-average intellectual function, to lack adaptive behavior skills and to have had these problems since an early age.

Dr. Denkowski conducted tests to determine whether defendants who might face the death penalty aligned with those definitions. But other psychologists and defense lawyers complained that he artificially inflated intelligence scores to make defendants eligible for the death penalty. (Dr. Denkowski’s lawyer has said that he vigorously denies having violated any psychology board rules and that he used his best clinical judgment in making forensic evaluations.)

Last year, the Texas Board of Examiners of Psychologists agreed to a settlement with Dr. Denkowski in which it reprimanded him, but he did not admit guilt. He agreed not to conduct intellectual disability evaluations in future criminal cases and to pay a fine of $5,500. In return, the board dismissed the complaints.

Since that reprimand, the Texas Court of Criminal Appeals has asked trial courts to review at least six cases that included Dr. Denkowski’s work to determine what effect it had had on the case.

Defense lawyers argue that Dr. Denkowski’s conclusions should be completely excluded from those reviews.

“You can talk all day long about how you don’t want junk science used in these cases, but when you’re confronted with it, you have to take active steps to make sure it hasn’t contaminated the case,” said Kathryn Kase, executive director of the Texas Defender Service, which represents death row inmates.

The Butler and Matamoros cases are the first to be returned to the Court of Appeals.

bgrissom@texastribune.org