Any of the PVA glues like Titebond waste much of the positive effect sinew can have on a bow. They do not allow the sinew to shrink and pre-stress the back.
Now if you simply need to back the bow because of ring violation (blankety-blank bugs, anyway) don't go thru the work of laying down sinew bundle by bundle when simple antelope or other thin rawhide will do the exact same job with far less work. Unless you have done a couple dozen sinew jobs, it's likely to turn out looking pretty much like burn scar tissue, too.* A rawhide back allows for nice place to work in some tribal style art or other fanciments.
And if you use Titebond III to glue down the rawhide, it will create a nice little vapor barrier for the wood. TB III can also go over the rawhide, too. Double your vapor barrier!
*I know eleventeen people are going to post that their sinew work is pretty. You are the exceptions that prove the rule.
