Try rubbing alcohol on a q-tip. You might have to really work at it to get it off the grout. Don't rub it in with heavy downward pressure, rub lightly and try to 'lift' the paint out of the grout, it that makes sense ;) Switch q-tips frequently as paint begins so dissolve and lift. Or you could try putting a little rubbing alcohol right onto the paint, let it sit for a minute or two, then dab at it to lift the paint off. There's also "Goof Off", although I'm not sure if it works on grout without harming it (be sure to check the label). If you have heavier solid drops of paint (vs. tiny splatters) try first to pop them off with a fingernail or a super thin metal putty knife with a layer of thin fabric (an old t-shirt is ideal) wrapped around the end so it doesn't scratch/gouge tile or grout. Fabric/rag must be damp, not dry. Use one hand to hold the putty knife and rest a couple fingers from the other hand on top the putty knife as a guide, hold it at near level with the paint drop, slide the putty knife under the paint drop and it should pop right off (be careful if you use the putty knife, carelessness could scratch the tile/grout).

Thanks, Moonshadow!

It was mostly little splatter (I would have noticed otherwise). It's coming off pretty nicely with a knife. I did not think to wrap a fabric around it and did scratch the tile a little in one place. I have two more areas to do and will follow your suggestion.

Thanks again!

You're quite welcome ;)