Mike George
To get rid of pitting you have to remove metal. Unfortunately the holes can’t be filled in.

Metal can be reamed or ground out, but the barrel walls may not be thick enough to allow this process without rendering the gun unsafe to submit for re-proof.

All I can suggest is that you take your gun to a gunsmith and ask for an opinion.

It might also be worth contacting that excellent engineer, Nigel Teague to see if he can help; Nigel has developed a process whereby Damascus barrels are bored out, then a steel tube inserted.

This means the gun is safe to shoot and still retains that lovely Damascus patterning on the outside.

Call him on 01454 260226.