Hi, Libby!
I was just passing through and noticed your post, thought I'd throw in my two cents! :o)

We have found several egg cases around here, and since I knew they would probably be mowed down, I've moved them. I sometimes will take the stick/stem it's attached to, and stick it in the ground somewhere else. I've also stuck them in with other plants in a container on my porch. I think yours will be fine. They hatch once the weather is warm, but I'm not sure of the temperature. We even had some hatch in the house this winter!!! (A praying mantis had been in the house last fall, she left an egg sac up inside the corner of a window. When the weather got cold, we turned on a heater near the window, and they hatched!)

Hoping you see lots of babies in your garden this year,
Angel

It is okay to re-position them anywhere. You should put them up off the ground, because ants like to eat the eggs. When I find them low down, I just put them in the crotches of trees.