I can see a couple potential ways around this.
Pry up the side away from the wall, shove the whole cover towards the wall, possibly pry up the underside/backside of the cover lip, pop off. That's assuming both are on the same side.
Long screwdriver though one of the holes on the opposite side of the box from the screws - have fun finding the head. A flashlight in another hole and your eye at a third might help. Philips might be a good guess unless they were really being nasty, in which case security Torx might be more likely. Try to look first.
Don't overlook pure misdirection. Could be the panel appears to open, but actually you slide it up off keyhole slots in the back. Would be kinda hokey, but I have run into some hokey stuff in consumer products that the maker wanted to become damaged if someone opened them the way that appeared to be the obvious way of opening them. Could be you push something to unlatch and it opens on a hinge rather like a rear access wall-mount rack.
or wait until a disgruntled ex-Brinks home security installer comes along and says....