What I'd do is head to a lumber store and get a length of hardwood dowel twice the diameter of the screw I intended to use. Drill a tight fit hole for the dowel(s) in the same holes that were used before, slather it with plenty of carpenters glue, tap the dowel(s) into the hole(s), cut them off flush. Give the glue 24 hours to dry. Then use a drill bit almost the same size as the new SS screws I was going to use to pre-drill the holes for use by the screws. Then use plastic washers maybe if the plastic sheet got damaged and the holes were torn a bit.
This all depends on how thick the plywood edge you're drilling into is. You do want some plywood on either side of the dowels of course. It's the glue that will do the work of holding things together in the wood.
Some measurements and a picture or three of your situation would really help get more answers. (The image above is blank).
