How long has it been since being painted? You may be able to soak the grills in a solvent and remove the new paint. The solvent could be as easy as water and some ammonia.

Beyond that, you could use paint remover and go back to bare metal. I had a floor convection heating system grill, probably from the 1800's that had been painted so many times that some of the holes were filled (these were not tiny speaker grille holes). It originally looked grisly. It was not quick and easy, but I went back to bare metal, then used rust remover and repainted with primer and satin enamel. The grille looked brand new. To some extent this was not the original intention for this antique because it had been blued, not painted, but black paint fit the current decore better than irregularly faded ancient bluing.

Painting the speaker grille will probably be a challenge unless you are skilled with airbrushing. My guess is that you (or the painter) would need to airbrush, then bake the enamel. Uniformly covering, but not clogging the sides of the holes is the tough part. Maybe dipping in somewhat diluted paint, then blowing the holes open with a gentle blast of air is a better plan.