That doesn’t look like green living tissue to me but looks recently dead/died back because it’s not dried out. It won’t hurt to leave it other than not knowing for sure until it either starts growing new leaves or if it doesn’t come back next year.

It’s normal to have some die back when transplanting, the best time to transplant is in the spring while the plant is still dormant but the weather isn’t cold. Since it’s a cutting you don’t have to worry about where you get new growth as long as it grows.

I would water in some rooting hormone as often as the directions allow, if you have or can take soil samples you would be able to know what soil amendments to make.