For pin knots I generally reject the strip as suitable for a backing. I usually make narrow longbows 1" or less wide and despite fattening the area around the knot on the bowstave(like you would with a tree stave) they broke, at the knot. You get the dreaded" tick" and sooner or later the bow blows.
You might have more success with a pin knot in a backing if the limbs were much wider, say 1&1/2" or more. You would still need to compensate for it by leaving extra width in the backing at that point.
You save more time and materials if you only use clear, straight grained, smoothed backing.
Rejects can be sawn up for billet backings or used as core wood.