Hi:
The photos are of a Hoover service tool for adjusting or bending of the early design agitator brush retaining end tabs. The agitator brush strips in some of the 1930's models did not use a retaining screw. The metal tabs of the agitator assembly fit in the brush strip grooves to securely hold the brush strip in the agitator roll under spring tension As, I recall the tabs would become bent and fail to retain the brush strip and it could be ejected while vacuuming the carpet. My father and I used this tool for vacuum repairs back in the 1940's, 50's and 60's.
The brush strip photo shows the retaining grooves on its extreme ends. There are also grooves located on the inner edge of the first tuft of bristles on each end as well. A screwdriver blade was fitted into these grooves to remove or insert a brush strip while applying downward pressure against the leaf springs visible in the agitator photo.
I believe the tool was offered by Hoover to servicemen, but the are no imprints of any sort on the tool.
( I used a wad of green 3M scrubbing pad to hold the tool in position for the photo shoot.)