Just putty over it and get a slightly matching high-gloss or semi-gloss enamel and nobody will notice it. I've put tons of holes in things in rentals over the years and basically nobody will care as long as you restore it to like condition when you leave.
Have you ever seen a landlord check that kind of things really?
Unless you have made a mess with wires getting out looking like a fire hazard in waiting I don't know anyone who would stop at 2 tiny screw holes. Heck the landowner may not even remember the unit was not made that way in the first place.