Here is a post with comments from Lenny Wells (UGA Pecan Specialist). Best control option is trapping.
This (squirrel injury) normally occurs on smooth-barked limbs or central leaders 3″ or less in diameter. The culprits here are flying squirrels. When food sources become scarce, flying squirrels will strip the bark off smooth barked branches to feed on the tree’s cambium. If they completely girdle the limb or central leader at any point on the tree, the limb or leader will die from that point upward. If the damage does not completely girdle the limb or tree, the wound normally heals over with time. Flying squirrels are nocturnal. Their home range is usually no more than an acre so damage tends to be isolated to certain spots in the orchard.
