Ballpoint ink has ingredients that cause it to adhere to surfaces. This permanence is important when the surface is paper documents or other places you intend to put the ink. When the same ink is scribbled onto a plastic surface the result can be an unwanted stain. Ink stains are easiest to remove while still fresh. You can use home remedies to remove the ballpoint pen stains from the plastic surface. If the stain is old, a little more elbow grease might be necessary, but you can still get clean plastic.
Wet a clean cloth with nail polish remover. Wring out excess moisture, and then rub the surface of the plastic at the site of the ink stain. Move to a clean portion of the cloth as the ink stain is transferred to the cleaning cloth.
Place a few drops of dishwashing detergent onto another clean, damp cloth. Scrub the plastic to remove the nail polish remover and ink stain. Rinse with another damp cloth and dry the surface.
Combine equal parts ammonia, lemon juice and water in a bowl. Add one teaspoon baking soda for a mild abrasive that won't scratch the plastic. Tackle any remaining ballpoint ink stain by scrubbing it with the lemon juice mixture until the stain is gone.
Rinse the plastic off with water and dry the surface with clean cloths.