Wash down with vinegar and spray with Lysol mildew/mold killer.
Try WD40 ON THIS TOO IT COMES IN AEROSOL CANS IT'S VERY GOOD
Try hydrogen peroxide. Do a test patch first
So far nothing has worked on my table.
Concrobium mold control, available at most home stores or hardware stores. Check to see if it can be used on your finished/unfinished wood. May take repeated applications and time, but is quite effective.