I had a similar issue with '50's era non-relieved target grips that were otherwise like new. Large as life left side below the grip screw in the checkering were two initials! They looked impossible to remove, but I recheckered over them and here's the result:
The added benefit was a more coke bottle shape/feel to the grips.
But the stag I'd have to see to come up with possible corrective action. I've removed chips and gouges by slimming/refinishing which most stags can endure and for the better. I've also filled voids or chipped off corners by grafting/splicing and gluing color matching pieces. This pair had a pretty large size corner broken off of the toe: