When you offer tile & grout cleaning & sealing services, I guess sometimes you have to expect questions like this: "Hello. We have an indoor stone floor with red paint on the grout. Can you remove it?"
I said I'd come and take a look. Looking for methods people have used to do this. Stripper? Gel?
Sand it off?

Try the thin brass/wire brushes for grout lines. Be careful though because it could damage the stone if you are to aggressive. That should take the top layer off, if its sanded grout and very pourous than it may be more difficult. If its ceramic, any type of solvent should not damage it.