How to rectify a wrong center punch

[Toolmaker51]

Frank S is absolutely correct. Peening out miss-markings is likely most common correct modern use of a ball peen hammer. Light taps are all that is needed to 'erase', actually move metal back where it was. Another good reason to get older ones when opportunity arrives, they were more hemispherical in the past, where cold metal shaping was common. Now they present more of a tapered configuration. Easier to hit [tap] small locations, maybe not so desirable for radiused forming...

I've got a light sense of touch. Center punching, I can feel the fine point descend into one scribed line, and move it into where axis cross. There are 3 such punches; prick which is nearly needle sharp, about 30 degrees included angle. That's too delicate for a real mark to hold a drill point or compass. There are two larger, about 60 and 90 degrees you can follow up with when needed. I use 60 for center drills, 90 for hand drilling.