I recently heard a rabbi speak about returning stolen funds. He said that rather than calling the police, the money could be returned anonymously. What is wrong with facing any criminal charges that you may deserve? Isn't that a part of repentance?
The Aish Rabbi Replies:
Excellent question! The idea is like this:
Since a human court cannot determine what is in the heart of man, they have to punish according to the rules of the book, irrespective of regret.
God, on the other hand, knows what is in the heart of man, so He allows for sincere repentance that literally wipes the slate clean. In the event that a person admitted their mistake voluntarily, they clearly have remorse - and the matter can remain between himself and God, as long as the proper financial restitution is made.
But taking your principle to an extreme, I should turn myself into the police station every time I exceed the speed limit!
Of course, there is the concept that suffering helps achieve atonement. The reason this works is that when a person inclines too far to their physical desires and transgressions, the natural reparation is to lose some measure of physical comfort.
In this case, I think it is more productive to make amends privately and resolve not to do it again.