I attached a piece of plastic canvas (available at WalMart or most craft stores) tightly to the diffuser using the smallest wire ties I could find. The holes are too small for the babies to get to the water. The stuff is cheap, I spent less than $5 on enough for eight egg tubs, and it can be easily cut with scissors.
Underside of the light diffuser:
Diffuser in egg box:
Folks also put either clean playground sand or aquarium gravel in the bottom not only to help stop the water from sloshing if you have to move the tub, but also to increase the thermal mass inside the tub which helps keep the temperature stable.