Leave it sit for a few days. It should work its way out. This is another reason I use Titebond III with my sinew. The tb seals the sinew off.
You're not in too bad of shape though. On my last bow, I sanded the sinew smooth and put an oil based stain on it. I let that dry and sprayed poly on it. It hasn't hurt the sinew one bit.
That was with TBIII though not hide glue. I'm not sure what effect it will have on hide glue.