Forget that that projection screen wasn't a white board? It's a common mistake, and, while removing those marks may be difficult, it's not impossible. Stain removal largely depends on the material from which the screen is made and how long the stain has been allowed to sit on the screen. Your success is more likely the sooner the stain is addressed.
Try using ReMarkable Whiteboard Cleaner. This product is designed specifically to remove dry erase ink. Be sure to hold a cloth under the area that is being sprayed to catch any drips and prevent the stain from spreading to other parts of the screen. Spray the cleaner and wipe the ink away. Repeat until the stain is removed. Do not let the screen get so wet that it gets damaged; allow it to dry between applications if necessary. When the stain is removed, wipe off residue with water and a soft cloth.
If the ReMarkable Whiteboard Cleaner fails to remove the stain, try the Mr. Clean Magic Eraser. This product has proven successful at removing a variety of stains, whether you're worried about dry erase ink or any scuff marks on the screen. Simply moisten the sponge and gently rub over the stain. Continue rubbing until the stain is removed. Once the stain has been removed, wipe away any residue with a little water and a soft cloth.
Try pretreating the stain. If the Magic Eraser is not successful, the screen may need to be treated with something first. Try wetting a cotton swab with rubbing alcohol and rubbing the swab over the area first, then try using the Magic Eraser again. If the rubbing alcohol does not help, try the same method with Simple Green. When finished removing the stain, wipe away any residue with a little water and a soft cloth.