Car door vinyl tends to be slightly porous and holds stains, like ink, tightly. The sooner you notice the ink and try to clean it, the better. After it has been baked on by the sun and heat of the car, it becomes increasingly more difficult to remove this kind of stain. You'll need to be patient when cleaning the vinyl; unless the ink is very fresh, it will take a while to remove. Persistence should pay off, however.
Fill a clean cup with cold water and add a few drops of washing powder. Use a detergent that claims it can tackle touch stains, such as ink.
Put on rubber gloves and, depending on the size of the stain, dip either a paper towel or a cotton swab in this cleaning mixture. Dab at the ink, covering it completely.
Use a fresh, dry paper towel to wipe the area. Try not to spread the fluid around, however, or you will spread the stain. If some of the ink came off onto the paper towel, use fresh towels and keep applying the cleaning solution, wiping off more and more.
Use rubbing alcohol, after you've removed as much ink as you can with the detergent and water. Just dip a corner of a dry paper towel or a cotton swab into the rubbing alcohol and wipe the area. This solvent should loosen ink from the vinyl, unless it has been on there for a long time, in which case, nothing may work, according to Procarcare.com. (See References 1)
Dump the cleaner out of the cup, then rinse the cup and refill with clean water. Use a fresh paper towel to rinse off traces of detergent or alcohol from the vinyl.
Instead of detergent, try an auto vinyl cleaner on the stain before using the alcohol. Look for vinyl cleaners at auto supply retailers. Use it the same way as the detergent cleaner: Apply it, then wipe it off.