go ebay and search 2 mm neoprene repair material or cut up a computer mouse mat. Both work usecontact adhesive for neoprene.
if the wood underneath is finished and presentable you could also just clean the rest of the foam gunk out and leave it, it's not really important for anything.
it's just there for when the bridge falls back while the strings are off, but ideally that shouldn't be happening in the first place. the player should be slipping a wedge or "chock" back there under the screws to hold the bridge level, that way the screws can be accessed with the wrench while restringing and there's less risk of the bridge jumping off the posts.