Both Dodd and the official, who asked not to be named, said it was because administration officials were afraid the government would face numerous lawsuits without the new language.
Dodd, a Democrat, told CNN's Dana Bash and Wolf Blitzer that Obama administration officials pushed for the language to an amendment
designed to limit bonuses and "golden parachutes" at those companies.
"The administration had expressed reservations," Dodd said. "They asked for modifications. The alternative was losing the amendment entirely."
On Tuesday, Dodd denied to CNN that he had anything to do with adding the language, which has been used by officials at bailed-out insurance giant AIG to justify paying millions of dollars in bonuses to executives after receiving federal money.
He said Wednesday that the "grandfather clause" language "seemed like innocent modifications" at the time. Video Watch Dodd's interview with CNN's Dana Bash »
"I agreed reluctantly," Dodd said. "I was changing the amendment because others were insistent."
Dodd said he did not speak to high-ranking administration officials and the change came after his staff spoke with staffers from Treasury.
The White House did not immediately respond to CNN's request for comment.