Long as it is not from the tendon from the neck of the cow.
Longer sinew from elk or deer back strap I would think would be more even tension on the backing.
If it's greasy just soak it in dish soap, rinse,then water. Use hide glue to get the natural adhesive back in the sinew.
weather resistant carpenters glue Works OK as well but must be cured longer because the glue dries faster than the Sinew.