Well, he can’t right his wrongs, exactly, but if he wanted to demonstrate that he has changed his ways, he might want to....well....stop gambling on baseball. And stop lying about gambling on baseball.
He is no longer a player or manager. He is John Q Public and betting on baseball is ok for John Q Public.
Now if they want to make that a condition for his getting into the hall of fame, sure. But no one has said that. At least I have never heard about it.