I considered them fine fodder for the cook pot, not vermin. I really enjoyed hunting them with a 22 rifle or pistol when I lived where they do (Carmel, CA - late 60's to mid 70's), and I hunted them often all along the central to northern coastal ranges. Used my Win 1890 pump, and starting in 1971 when I bought it just for them a Colt New Frontier Buntline covertable. I never used shotguns or my first muzzies in the early 70's that were TC 50 & 54 Hawkens. Closest I could come to them for hunting before those days or since is pine squirrels, plus prairie dogs, rock chucks and several species of ground squirrels which I did hunt extensively from the early 50's to just a few years ago.
When you want a squirrel meal, you want a squirrel meal, right? LOL In Carmel my place was on the beach/ocean front and had several Ponderosa pines and coast live oaks on it with a healthy population of Gray's. So a few times, when they lined up with the ocean backdrop, some would fall to my 1890 with 22 shorts so the neighbors wouldn't notice, and we'd have fresh unscheduled squirrel for lunch.
I would love a chance to use one of my 17HM2's for them, rifle or pistol. I've used them on several species of ground squirrels and jacks. They are heads above the 22LR, especially when the range gets long. So they are the perfect Gray squirrel cartridge IMO.