Just go ahead and recut the checkering right through what is there.
Trying to remove the finish that is just on the diamonds and not disturb anything outside the pattern is tedious. It usually results in some finish being removed
elsewhere outside the pattern.
Then you are in for touching up the stock finish itself.
That can be simple, or it can be one of those jobs that starts as a small couple of spots and ends up being an entire refinish.

It almost looks like a spray finish was applied over the stock and checkering together at some point.
Depending on what it is , it may lift at the edges of the checkering borders as you recut and chip/peel off of the surface of the adjacent wood surface as well.
..and it may be just the pic that makes it look as though it is..