Superficial pitting can be repaired
Early Syracuse Quality No. 3 extra heavy frame 10 gauge courtesy of Frank Cronin

After by Brad Bachelder

I'm with Steve and would leave that be. It is unlikely that the repair could be colored to match the Damascus pattern and would be very obvious.
There was a thread on the PGCA forum 1-2 years ago with before and after pics of a damascus barrel muzzle repair which was quite well done I believe by Peter Nagel. I have a before pic but couldn't find the after. Different location and quite different pressures.