Recut ,,I always recut the checkering.

It doesn't take much to dull any of the checkering cutters unless they are carbide type.
Even those get dull after a time but they zip thru any of the stuff pretty well.

I'm usually not all that careful around the checkering when scraping and sanding. I go right over and onto the patterns knowing I'm going to recut them.
If you don't the finished wood can have a slightly different look right around the outside of the checkering border where you were 'xtra careful' when doing the prep.
If you have a tendency in backing off a bit & trying not to damage the checkering, you use lighter pressure in scraping and sanding. Just generally less of it too.
The wood color can end up being slightly different surrounding the checkering patterns.
Have at it, do the job, and recut the checkering to finish it off.