All of these suggestions, and no one has bothered to ask, "What kind of paint did you use; latex or enamel?". If it was latex, the answer is very easy, soak them in warm water until the paint softens then gently scrub them with an old toothbrush. If you used enamel and your grills are plastic, try using lacquer thinner. A word of caution though, put a little of the thinner on a Q-Tip and dab it on the backside of the grill first to see if the thinner will damage your grill. If it doesn't great, use rubber gloves and some old rags and clean away. If the thinner just messes up the surface of the grill, use it anyway because you're going to paint the grills, but be gentle and take your time. But, if the thinner softens or melts the plastic, just contact the speaker mfg and order new grills.
Good luck!