CS Master's admission after academic dishonesty
Based on what you stated, it doesn't really sound like this will follow you anywhere. You were caught, they gave you a token punishment, and everyone moved on. It's not as though you have to state your dishonesty on your resume or whatnot. I would recommend treating it as a lesson learned, and unless someone specifically asks you about it, don't bring it up.

To directly answer your questions... no, you really can't do anything to fix it. It's part of your history now. However, it may not affect your application, as they receiving university will probably never find out about it.

Note that all of this is based on the assumption that your dishonesty does not go on your official transcript, based on your having stated that in the question text. If it is on the official transcript—the one that one university will send to another when asked—then your situation is a good deal worse.