Heating sinew to steam temperature will denature the proteins (in other words, cook 'em) once they have a little moisture back in them. Ever try to rehydrate sinew strands in hot water? They shrink up, bulk up, and never work right. I have tried to recover sinew from a bow and was utterly frustrated by the cluster-flustered mess it became. I ended up simmering the whole mess down when I made the next batch of hide glue. Trust me, you could have reflexed a dozen bowlimbs with what came out of my ears and toasted another dozen hickory bows with the blue streak of cursing outa my mouth. If you had used hide glue or unflavored gelatin (another form of hide glue), I would say scrape it off, rehydrate and simmer it down slowly, recycling the hide glue and converting the sinews to more glue. I believe TBII is a latex derived compound so I do not know if you will ever be able to isolate the sinew from the glue.
All you composite bow makers out there...Ever heat bend a sinewed limb???
Good luck whitewoodshunter, keep us posted on your results.
(and a side note...I am always amazed by how we bowscrapers turn ourselves inside out to reveal our own 'tricks of the trade' rather than hoard our hard-won knowledge and experience)