Eggs in soil of indoor peace lily-what next?

Having seen the plant in it's pot, I think you have two choices either take it back to the shop now, or start the process again if you want to save it.

First..... Peace Lilies grow into large plants and I think the pot you have it in is too small which means it's roots will be crammed. Second....If you want to save it, take it out of the pot, remove all the soil and wash the roots off completely, you can do that in the garden. Then re-plant it in fresh soil. Peace lilies don't like the cold or draughts, could that be a factor as well?

 

These eggs, have you tried squashing one/opening one up?