captaincvx -
If your solid osage bow was originally a 1940s era Bear Bush Bow, it was greatly altered at some time in the past. Your close up photographs show what appears to be some finely woven gauze like material under the black outer coating immediately below the handle section on the lower limb. That area was likely cracked and then repaired. The fact that the solid black material is cracked and flaking off, indicates to me that it is simply a thick black paint or some type of early black rosin. The backing is clearly rawhide not sinew.
The lines of the bow, at the fadeouts of the handle section and outline of the bow, and the belly of the upper limb, all appear to have been scraped down, likely to clean up the damaged area and to reduce the weight of the bow keeping the limbs evenly tillered. It is also possible the original intent was to simply reduce the weight and some inadvertent damage occurred during this process that made the repair necessary. The fact that there are no markings on the bow, likely means while scraping the belly of both limbs of the bow, the markings were removed which would have been on the belly of the upper limb just above the handle section, if it was a Bear Bow. Judging from what is left of the bow, if it was originally a Bear bow, it was marked “Bear Archery by Grumley”.
With over a 100 Bear Grumley bows in the bow collection here, and having owned, examined and handled dozens of other Grumley bows since I began accumulating archery stuff in 1958, I can attest to the fact that many Bear Grumley era bows exist today in repaired condition, and many exist without their original markings.