Blend 1/4 cup powdered dishwasher detergent with enough water to make a thin paste. Spray the brick veneer surface with water from a spray bottle. Dip a toothbrush or small scrub brush into the paste and scrub the paint stain until it disappears from the surface of the brick veneer. Rinse the brick veneer with plain water.
Cut a rag to slightly larger than the paint stain. Saturate the rag with paint thinner and lay it over the paint stain. Let the paint-thinner-saturated rag remain on the paint-stained brick for two to six hours. Check the condition of the paint every 30 to 45 minutes to determine if the paint is becoming soft. Scrape the paint stain with a paint scraper or wire brush to remove all traces of the stain. Rinse the bricks with water and scrub with mild dish detergent. Rinse the brick veneer a second time to remove paint thinner and soap residues.
Dip a paintbrush into mineral spirits and apply a thick coat over the paint stains. Let the mineral spirits lift and bubble the paint. If the brick veneer is outdoors, spray the surface with water through a pressure nozzle attached to a garden hose. If the brick is indoors, dip a nylon scrub brush into water and scrub the paint stain off the brick veneer.
Spray the paint stain with a commercially available paint remover specifically made for graffiti removal on masonry surfaces. Follow the paint-remover manufacturer's directions to determine the length of time to leave the chemical on the paint stain, usually 20 to 60 minutes depending on the brand. Dip a nylon scrub brush into water and scrub the paint stain off the brick veneer. Scrub the brick veneer with mild dish detergent and rinse with water.