Redemption is the act of doing something that makes people have a good opinion of you again after you have behaved or performed badly.
Absolution is the act of forgiving someone, especially in the Christian religion, for something bad that they have done or thought:
Absolution is a religious concept for purging someone of sin, granting them absolution. The word is used for other kinds of forgiveness too.
Atonement, atoning, or making amends is the concept of a person taking action to correct previous wrongdoing on their part, either through direct action to undo the consequences of that act.