That's a tough one.. what kind of finish?.. spray on poly, rub on finish?
I would lightly sand that area with fine sand paper.. try to get some of the depth out of it..
You could dry a little super glue.. fine sand then do a single finish over that area.. Min wax makes a rub on poly.. works good.
That's why I like Tung oil.. I can sand it all the way down back to wood in one spot.. rub on some more tung oil and never see it.