Ohio State trustees learned of Gee's "offensive statements" in January, met with the president at length and created the remediation plan, Schottenstein said.
Gee was on a long-planned family vacation and unavailable for comment, Ohio State spokeswoman Gayle Saunders said. He apologized in a statement released to the AP.
"The comments I made were just plain wrong, and in no way do they reflect what the university stands for," he said in the statement. "They were a poor attempt at humor and entirely inappropriate. There is no excuse for this and I am deeply sorry."
Gee told members of the council that he negotiated with Notre Dame officials over joining the Big Ten during his first term at Ohio State, which began more than two decades ago.
"The fathers are holy on Sunday, and they're holy hell on the rest of the week," Gee said to laughter at the Dec. 5 meeting attended by Athletic Director Gene Smith, several other athletic department members, professors and students.
"You just can't trust those damn Catholics on a Thursday or a Friday, and so, literally, I can say that," said Gee, a Mormon.
In the recording, Gee referred specifically to dealing with the Rev. Ned Joyce, Notre Dame's longtime executive vice president, who died in 2004.
"Father Joyce was one of those people who ran the university for many, many years," Gee said.
Gee said the Atlantic Coast Conference, which added Notre Dame in all sports except football and hockey, did so at a time when it was feeling vulnerable.
"Notre Dame wanted to have its cake and eat it, too," Gee said, according to the recording and a copy of the meeting's minutes.
"Regrettable" and "inappropriate" summed up the reactions from universities mentioned by Gee at the meeting, including Notre Dame, Louisville, Kentucky and schools in the Southeastern Conference.