I think I found a praying mantis egg case when I finally cut the dead vines from my bad homemade trellis. I really wanted to redo the trellis for next year - but I don't want to hurt the native mantises - especially after the Japanese Beatle issues I had this spring -early summer ! Will removing the dead vegetation cause them to be too exposed over the winter - if so - what can I do to protect them? If I dismantle the trellis - will that kill the eggs?
It's about an inch long - here's the 2 best pics -

If you can dismantle the trellis without damaging the case, just tuck that pole into a shrub that won't be disturbed till spring. It should be fine.

I'll look at it tomorrow and see .... It won't be hard to take apart - I'm just concerned that the egg sac is in the corner where it might be easy to damage it. How sturdy are they when moving stuff around very close like that? Are they at least somewhat tough or are they pretty delicate?

They seem pretty tough. Go ahead and touch it to feel how rigid it is. I think some people actually remove them from whatever they're attached to, but I haven't. I've moved many attached to branches and, although I was careful, I didn't worry about damage.