Painting accidents happen. It is almost inevitable that flecks of paint will end up on objects and areas that you didn't intend to paint. If latex ends up on tile, this is rarely a big deal, even if the paint dries. Latex paint comes up rather easily off tile and other hard surfaces. Grout presents a bit more of a challenge, however, because it is very porous material (unless it has been well sealed). Fortunately, since latex is a water-based paint, even when dried it can usually be removed if you use the proper methods.
Carefully remove the pieces of dried latex with a razor blade. The more you get out this way, the better.
Pour a little rubbing alcohol on the paint. Give it several minutes to soak. Press it with a paper towel. If it starts coming off (and it should), then add more alcohol and keep dabbing with a fresh paper towel.
Wet a cloth with some dish soap and water. Wash the grout. Some more of the paint should lift up this way. Change to a clean section of the damp cloth on a frequent basis.
Wet a toothbrush and pour a bit of dish detergent directly on the bristles. Scrub off the remaining traces of paint with the toothbrush.
Rinse the grout with clean water. If any small flecks of paint remain, use alcohol on it again and brush with a toothbrush until it is clean.