The only thing I know of that kills flea eggs is Revolution, a topical pesticide that will get rid of fleas, flea eggs, earmites and ticks.

Dawn won't do anything for fleas and flea eggs. When I took Mandy to the vet, she was loaded with fleas and flea eggs. The vet told me to put Revolution on all my cats. He said that if any flea eggs hatched in the house, they'd hop a ride on a cat and die.