When former President Donald J. Trump appeared before an appeals court in Washington this week to claim he was immune from prosecution for his efforts to overturn the 2020 election, one of his lawyers argued that he should not face criminal charges because the Senate had failed to convict him of similar offenses at an impeachment trial three years ago.

But at that February 2021 trial, Mr. Trump, through a different set of lawyers, made the opposite claim: He argued that the Senate could not convict him because he was already out of office, while pointing to the criminal justice system as the legitimate remaining way to seek accountability.

“After he is out of office,” Bruce Castor, one of the impeachment lawyers, said, “you go and arrest him.”

This seeming contradiction was among the complexities about Mr. Trump’s immunity claims that caught the eye of the judges on the U.S. Court of Appeals for the District of Columbia Circuit on Tuesday. A three-judge panel hearing his challenge to the election subversion case charges seemed skeptical of the argument.

The judges explored the apparent disconnect with D. John Sauer, a lawyer who handled the appeal for Mr. Trump. They pressed him to explain why the former president appeared to have reversed himself so drastically.

“You took the position — or your client did — during the impeachment proceedings that there would be an option for criminal prosecution later, and it’s in the Congressional Record,” said Judge Florence Y. Pan.