Yep, I process the sinew and then I wash the back just like Pat said, then I wash all the sinew in bundles pre sorted for amount and length that I also separate for each limb on separate boards after washed and rinsed.
One thing I have started doing is getting a pot of hot water by my glue pot and I dip each bundle in the hot water and ring it out good before it goes in the glue. I think it helps to warm up the wet sinew before hitting the glue and helps keep the glue pot from cooling off too quick. After a few bundles of cold wet stuff it was loosing heat quickly.