That was not a wise decision to go in blindly with something you were not familiar with, but we all live and learn. Now you know "what not to do" the next time you come across this situation. To be honest with you, depending how long you let it sit to cure, will determine how difficult it will be to resolve the issue.
Most average people don't do any prep work when applying the touch up paint, because it did not adhere as well to the paint, that will be our advantage in this scenario. Touch up paint from the bottle is not as strong as the ones a body shop can make, but the paint resin, enamel, catalyst, is pretty decent for a consumer based product.
Usually touch up paint will completely dry to the touch within 1-2 hours, depending on environment temperature as well, which will play a role in the curing time. But, even though it's dry already, you can still clean it off with some thinner, or acetone.
From the least aggressive method, I would recommend using some thinner to see if it works or not. Afterwards clean the area off with some soap and water because you will leave a film behind on the paint.
Follow it up with some compound from the auto parts and rub it with moderate/a lot pressure. If that fails you might have to invest some money into this system.
http://www.langka.com/index.php
Edit:wetsand would be your last resort.
