Here's a method for removing egg stains that I find works very well.

Soak the egg-stained material in warm water to help loosen it up. While it is soaking, create a paste of cream of tarter and water. Crush a couple aspirin and add them to the paste.

Once you are done soaking, apply the paste to the egg stain and allow it to sit for half an hour. Rinse well in warm water and your egg stain will be gone.