You can hard boil the egg, take off the shell, mush or chop it up a little and feed it back to them. It seems weird but the eggs are very good for them and will assist in egg laying (well, because eggs are good in protien, any future eggs that she lays will have the right amount of protien).
My ducks will eat them, but they like chicken eggs better. If not, if you have a dog... give it to him/her. My first dog would only eat hard boiled egg, but the dog I have now would pick them out from under the duck if she could. She just sits there licking it.
Eat them and enjoy the fruits of the all the water dumping and pool cleaning. Never have understood why people suggest feeding them to the dogs or back to the birds. We enjoy the eggs first, extras then are offered to the dogs. (there are never extras lol)