Really don't think you mean "overlay".
An overlay has the playfield art printed on it. It's used to restore a worn playfield and is installed to a bare wood playfield after sanding the damaged artwork off.
Seems like your game had a sheet of clear sticky mylar applied to protect the playfield. Sometimes the playfield is waxed prior to installing the mylar to make it easier to remove the mylar at some later time. But wax would clean off fairly easily, since it's wax.
Residue that's hard to remove really sounds like leftover adhesive and not like wax. There may have been mylar in other areas before you got the game.
Search removing mylar on here. Lots of tips for removing the adhesive.

Nice looking game.