He used to wipe over his khuffs without having put them on in a state of purity
If the situation is as you describe, that you wiped over your socks after having put them on when you were not in a state of purity, because you were unaware that that was required, then you do not have to make up those prayers according to the view of a number of scholars, but if you are able to make them up, that is better and is more prudent.