Well, generally speaking, it is dangerous and harmful to have makeup in your contact lenses. To clean the makeup off the contact lenses, first, you need to gently remove the contact lenses off your eye. And then squirt the contact solution all over the lenses. In the end, you should gently rub the makeup off with your fingers. By the way, to avoid getting makeup stuck in the contact lenses, you should put in your contacts before your makeup, and then take them out before you remove your makeup. In that way, you won't damage your eyes, contacts and they won't get dirty. And also, it doesn't really affect your makeup routine. Of course, having waterproof makeup can also help because it's less prone to smearing and getting into your eyes.
Ok, I can see that you are quite concerned about your contact lenses and are wondering whether it could still be put to use. So, as a matter of fact, a bit of makeup simply does not impede your use of it. You could just try to soak and wash your contact lenses with some solution. Just flush it with clean water and then put it in the solution. But if the situation is terrible, just discard it lest anything bad happens.
When you get the makeup in the surface of the contact lenses by accident, you will feel uncomfortable at the eyes. You should take the contact lenses out of the eyes and then use the solution to wash the contact lenses. After the makeup on the contact lenses is washed off, you could wear it again. Or else, your eyes will feel itchy and uncomfortable.