Bruce, be sure the sinew sheet conforms to the new back completely. You may want to rehydrate it first so it is flexible.
Ryan, I removed the sinew from a yew paddle bow that broke at the handle. I soaked the bow pieces in warm water and once the hide glue softened the sinew lifted right off. I reused the sinew but not in sheet form. I separated it and laid it out to dry. Once it was dry I stored it in a big ziploc then reused some of it on o0ther bows and save some for arrow wraps. It was back sinew.