Yes, it does resemble poison ivy a little bit but I've not heard of anyone getting a rash from peppervine. There is a huge bunch of it on our fence and it has not bothered me. I get a rash from a lot of plants that don't usually bother others, so it's a pretty good testimonial. If you don't want it, that's understandable. Peppervine can get enormous.
Poison ivy only ever makes 3 leaflets. Your pic shows leaves with 5 leaflets. There are some pics here:
Poison Ivy (Toxicodendron radicans)
It would be easy for some poison ivy to be hiding in there along with the peppervine, so look closely for slightly different looking leaves if you get in there to cut or dig the peppervine out. Another method is to find the main stem, cut it, then immediately paint brush killer (with a tiny paintbrush) right onto the cut. Easy to do, and uses a minuscule amount of 'cide.
Betony roots are edible and the foliage is benign, harmless.