Save yourself some work. Sand it out smooth and do it right! Or not rechecked at all.
I've done the rework thing twice. Both sucked. Maybe it was just me, but I sanded them both down and did it right.
Be it noted I hate checkering, and other than touching up existing work no longer checker my stocks. Makes no diff in the field and I happen to like the looks better. And it's a he k of a lot easier to refinish as needed.
Far easier than trying to sand to depth is to raise the old impressed checkering... Sand a little of the finish off so the ridges have their tops cleaned off then with a damp rag laid on the checkering and a towel on that press it with a hot, hot iron. Most of the impressed areas will start coming up. The old finish will prevent a full raising, but by sanding lightly as it comes up it will gradually increase in speed swelling up.
Generally it will leave good lines to follow and come right up to flush.
