Inspect each corner of the Lucite for any corners of the masking that have peeled away from the surface. It's not uncommon for a corner to loosen during the cutting process that is completed to cut the Lucite to size. If the corner has peeled up, peel the masking from the corner to the opposite corner of the Lucite to remove the masking completely.
Peel a small part of the masking away from a corner by placing a flat razor between the Lucite and the masking, if a corner has not been peeled away from the manufacturer process. Pushing the razor blade between the two materials will allow you to peel the masking away with your fingers.
Clean the Lucite with clean water and a cotton towel to clean the plastic and to remove the static cling often left by peeling the masking off of the Lucite. This will prevent dust from clinging to the glass.