Scrape dried latex paint off the surface of your untreated grout with a razor-edged scraper. Slowly and gently scrape the surface to lift as much of the paint as possible.
Brush the grout with a dry toothbrush. Repeat as necessary to remove the paint.
Dip the toothbrush into a bowl of rubbing alcohol. Apply the alcohol to the remaining latex paint on the grout. Scrub to loosen and remove the paint.
Moisten a dry cloth with three or four drops of baby oil. Rub the baby oil into any last traces of latex paint to remove them.
Wet the toothbrush. Add one drop of dish detergent and one drop of oxygen bleach to the toothbrush. Scrub the grout to remove the baby oil. Rinse the grout with water.
Blot the grout with a dry cloth to remove moisture. Allow the grout to air-dry.