I would imagine that most gunsmiths would (or should) polish those shallow pits out before re-bluing. I had an old Win M12 shooter re-blued and, without having to say anything to the smith, he polished the blemishes off of it before re-bluing.
Are you considering rebluing this 870 or just wondering what can be done? The gun should work just fine and it was designed to be a tool, not a showpiece. I’ve seen people improve things to the point of disaster. I’m just saying be careful so you don’t buy damage.
Good luck either way.
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