I am processing some whitetail leg sinew and noticed after pounding it flat and separating the sections that there is an oily feeling to the outside casing.  Should I remove this , washed it off, or just let it alone?

I generally discard the outer sheath as it doesn't provide long fibers.  The inner fibers should not have much, if any, grease on them.  I have never had to do anything other than strip the fibers apart.

I wash shredded sinew before using it with Dawn dish soap and warm water to remove any grease that might be on it. It doesn't seem to affect it for storage.

Thanks for the info John & Pat, I only have two leg sinews done so far and about fifty more to go.  A lot of pounding and shredding to do.  Now I know why the pre processed stuff costs so much.