My first thought too was that they are craving the protein or the amino acids/vitamins in the eggs. The other thing was I'd never heard of an egg eating goose!!
You'll have to do a couple of different things. One is to break the little behavioral chain (see egg: eat egg). This is an ongoing problem with chickens, and I've heard that getting rid of the egg eater is about the only way
. Geese aren't as nimble and mobile as chickens, so you could rig up a short barrier to the nests that chickens will jump over but will stop the geese.
I thought too that perhaps they are craving the protein. I think it's possible, but it's less of an issue. Think about it, an egg is the perfect food, a perfect mix of easy nutrients, amino acids, fatty acids, protein. It's a miracle more eggs aren't eaten, really lol.
Just in case, give the geese a handful of dog food. I haven't met a goose that didn't love dog food. It can't possibly be all the good for them, they don't need all the protein and fat in it, but maybe it will decrease the egg eating impulse.
Another idea is to make fake egg bombs (just letting my mind go nuts here
). Blow out an egg and then fill it with something noxious, like tabasco sauce.
Geese have elephant memories. I doubt they'll "forget" about eggs. Maybe aversion, extra protein and a good goose barrier will solve your problem.