Option 1:
If you leave it on, it will take hours to polish it by hand to get it to anything acceptable.
Ideally you would use a high speed drill with a mini buffing tool attachment and Novus 3 or other cutting compound to clean it that will fit in between the white bumper bases. Most of the topside of the upper playfield will need to be stripped anyway to get in there.
Option 2:
I opted to remove the mylar altogether and not replace it, as in a home environment it will be fine. Use De-Solv-It to weaken the glue, wait for the desolvit to work its way in and then peel the mylar away at a 180 degree angle.
The mylar around the bumpers is one piece and extends across to to the single drop target on the right, so you need to be a bit careful on those arrow inserts as the mylar will want to lift up the insert art when you peel it away.
The bonus is the art underneath looks factory fresh once the mylar is removed.
PS: Not sure if you are going custom or not, but those red bumper caps are from a Data East machine.