Small nicks can be sanded out with either sandpaper or a pumice stone (I have used the ones you buy in a chemist for your feet).
Larger nicks might require gluing back down - contact cement is probably your best bet.
When trying to figure out whether it is a big or a small nick, just imagine what the divot would look like if you sliced the leather flap off. If it looks shallow enough to sand out, then do that. If you think it would be too deep to sand, try gluing the flap back down. You are aiming for a smooth-ish surface, whatever you do.
If you sand or pumice, do make sure that you are careful to remove all traces of the sanding material from the strop afterwards, as if you do not your strop will become an abrasive.