I'm having trouble finding the splinter in the pic.  But, generally, if the splinter is in the working part of the limb, I would personally go down another ring if I had the wood to do so. A pristine back is a must for me, and starting a bow without that is like driving around on a tire with a chunk of rubber missing.  A patch wont fix it.  It's gonna blow, only question is when.  Having said that, if it is in the handle and the handle doesn't bend any, I wouldn't give it a second thought.