No, it isn't possible as far as just clicking and undoing it. MSPaint only allows 3 undo's and deletes the rest as you continue to click - and this is only saved for the time that person is editing the photo. Your ONLY option would be to get photo-editing software and restore the picture manually. Painstaking, but it can be made easier with good software and a little knowledge.
Check out Gimp 2.6
Related Link: http://www.gimp.org/macintosh/