I get some wood glue on a toothpick and put down in the hole as far as it will go. Then I pull it back up just a tiny bit and cut it off flush with flush cutters. At that point I push it back down into the hole so the toothpick is slightly below the level of the playfield. That way it leaves a tiny amount of hole up top for the screw to find when you are reassembling the playfield.

Yeah the glue helps solidify the whole area. I should have mentioned above that I always use the blunt end of high-quality round toothpicks because they fill the holes better and more solid.