Dude, he didn't say Grandpa bought the gun new in the 1920s, just he bought it then. Further, there was a time when taking a hawk or an owl was actually encouraged by various fish and game departments, as they had bounties on them.
Maybe one of the experts shall speak, but, with 32" barrels, that semi-pistol and the shape of the bottom of the frame, I'd guess a Baker.
I can't get very much from the photo.

Best,
Ted