Greenish bits in egg white

[jjdobbins]

Sorry I don't have a pic, but I'm hoping someone can explain why I occaisionally find this greenish bits in the egg whites. They are only in the Easter Egger's eggs, which have green shells...If I happen to boil one of these eggs I will find a grey bit that almost looks like gravel. She also has trouble with calcium deposits on her shells. Could this be related?

 

[RussianChickens]

Are the greenish bits hard like shell? Or just green spots?