How long has the paint been setting? An amonia based solvent will attack partially cured latex paint, usually without damaging the factory paint.

Poking the holes is tedious and probably will not look quite right unless the walls of the holes are uniformly covered (not likely).

Ultimately, this is the painter's fault, even if the customer or the designer demanded that the grills be the same color as the room, the painter should have known how hard this is to pull off -- and if the holes fill, it's not hard to guess that things are going south and the best plan would be to act before the paint dries.

I wonder if the 1812 Overture, played at full volume while the paint is wet, would help.