A report about a covert effort to delay their release until after the 1980 presidential election drew anger, resignation and disbelief from the survivors of the crisis.They are the last survivors of an international crisis that hobbled Jimmy Carter’s presidency and may have cost him re-election. Many are now in their 80s.With the former president gravely ill in hospice care, some of the 52 Americans who were held hostage in Iran for 444 days are looking back on Mr. Carter’s legacy with a mix of frustration, sadness and gratitude.Many feel neglected by the government, which has paid them only about a quarter of the $4.4 million that they were each promised by Congress in 2015, after decades of lobbying for compensation, said their lawyer, V. Thomas Lankford. Some endured physical and mental abuse, including mock executions, during the hostage crisis. About half have died.Jimmy Carter preparing to address the American people from the Oval Office on April 25, 1980, on the failed mission to rescue the Iran hostages.Associated PressLast week, their ordeal was thrust back into the news with the account of a covert effort to delay their release until after the 1980 presidential election in a bid to help the campaign of Mr. Carter’s Republican challenger, Ronald Reagan.A former Texas politician, Ben Barnes, told The New York Times that he had toured the Middle East that summer with John B. Connally Jr., the former Texas governor, who told regional leaders that Mr. Reagan would win and give the Iranians a “better deal.” Mr. Connally, a former Democrat turned Republican, was angling for a cabinet position.Mr. Barnes, 84, said that he was speaking out now because “history needs to know that this happened.”He told The Times that he did not know if the message that Mr. Connally gave to Middle Eastern leaders ever reached the Iranians, or whether it influenced them. Mr. Connally died in 1993. Nor was it clear if Mr. Reagan knew about the trip. Mr. Barnes said Mr. Connally had briefed William J. Casey, the chairman of Mr. Reagan’s campaign and later the director of the Central Intelligence Agency, in an airport lounge after the trip.The account stirred anger among some of the former hostages, while others dismissed his story of election sabotage as not credible. They are a diverse group that includes former diplomats, retired military officers and academics, and members of both major political parties.“It’s nice that Mr. Barnes is trying to soothe his soul during the last years of his life,” said Barry Rosen, 79, who was press attaché at the embassy in Tehran when it was overrun on Nov. 4, 1979. “But for the hostages who went through hell, he has not helped us at all. He has made it just as bad or worse.”Mr. Rosen, who lives in New York, said that Mr. Barnes should have come forward 43 years ago, given the decades of speculation about political interference.“It’s the definition of treason,” he said, “knowing that there was a possibility that the Carter administration might have been able to negotiate us out of Iran earlier.”Kathryn Koob, 84, of Waterloo, Iowa, who was the director of an Iranian-American cultural program when she was taken hostage, said, “If somebody wanted to be so cruel as to use us for political gain, that’s on their conscience, and they have to deal with it.”That Mr. Connally could have been engaged in political skulduggery was hardly shocking after Watergate, said John W. Limbert, 80, who was a political officer at the embassy when he was taken hostage.“It’s basically just confirmation of what we strongly suspected all along,” Mr. Limbert said. “We should not be surprised about this in American politics — people willing to stoop to anything.”He credited Mr. Carter with showing patience during the crisis, even if voters blamed him for mishandling the showdown with Ayatollah Ruhollah Khomeini, the Iranian leader whose followers stormed the embassy after the Carter administration admitted Mohammed Reza Pahlavi, the deposed shah of Iran, to the United States for medical treatment.“He basically sacrificed his presidency to get us out alive,” Mr. Limbert said.But Kevin Hermening, a certified financial planner in Mosinee, Wis., who was a Marine Corps sergeant guarding the embassy, said that he did not believe Mr. Barnes’s account and that, even if it were true, the effort would not have influenced his captors.“The Iranians were very clear that they were not going to release us while President Carter was in office,” said Mr. Hermening, 63. “He was despised by the mullahs and those people who followed the Ayatollah.”And Don Cooke, 68, of Gaithersburg, Md., a retired Foreign Service officer who was vice consul at the embassy, called Mr. Barnes’s account “mildly amusing.”It suggested, he said, that there were “these other dark forces that were sabotaging our efforts to get these hostages free, and I just don’t buy that.”Mr. Cooke still blames Mr. Carter for the crisis. He said the president should have cleared the embassy of its personnel before he admitted the shah or have refused to allow the shah to enter the country.When Mr. Carter flew to Rhein-Main Air Base in Germany to greet the freed hostages, Mr. Cooke said he snubbed the former president, staying on the phone with his parents as Mr. Carter put a hand on his back. He handed the phone to Mr. Carter, who spoke to his mother.“The reason we were released was because Ronald Reagan was elected president,” Mr. Cooke said. “The Iranians were clearly afraid of Reagan. No question about that. And they had every right to be.”Ben Barnes, left, with Lady Bird Johnson and former President Lyndon B. Johnson in Austin, Tex., on Aug. 29, 1970.Ted Powers/Associated PressThe hostages were released on Jan. 20, 1981, minutes after Mr. Reagan took office.It was the end of an anguished chapter. Network news anchors had kept nightly counts of how long the hostages had been in captivity, accompanied by martial music and “America Held Hostage” graphics. People across the country tied yellow ribbons around trees in a show of support for the hostages.After months of fruitless negotiations, Mr. Carter had authorized a rescue mission in April 1980 that ended in disaster when a helicopter crashed into a plane in the Iranian desert. Eight service members were killed, and their charred bodies were displayed by Iranian officials.In the end, Mr. Carter did not pull off the pre-election “October surprise” that some in Mr. Reagan’s orbit feared. It was only after Mr. Carter’s defeat that his outgoing administration struck a deal that released billions of dollars of frozen Iranian assets.Those assets were “the weapon that kept us alive,” said Mr. Rosen, the former press attaché. Referring to Mr. Carter, he added, “I think the thing he did — and did absolutely right — was to free the American hostages without us getting murdered.”The Barnes account cast a new light on these long-ago events, troubling David M. Roeder, a retired colonel who was the deputy Air Force attaché at the embassy. Mr. Roeder said that he had repeatedly told his captors that if Mr. Reagan won, they would be dealing with a “much tougher person.”“I have come to the conclusion — perhaps because I want to — that hopefully President Reagan was unaware that this was going on,” said Mr. Roeder, 83, of Pinehurst, N.C.But, he added, “I gained a great deal more respect for President Carter because I’ve seen what he went through with us in captivity.” More