Here in the UK, the Grey Squirrel is a pest. They are not native to Britain, and have driven our native Red Squirrel almost to extinction. There has been a massive drive, over the past ten years or so, to re-establish the Red in certain areas, together with a parallel drive to oust the Greys by culling them. (Which, of course, is euphemistish for kill the varmints!)
As to eating them, their meat is quite pleasant. A bit sweet for my taste, but not bad. The only problem is that you new quite a lot of them to feed a family of four! Next month is probably the best time to eat squirrel, as they have beenn fattening up all summer on order to survie their hibernation.

I'm immortal until proven otherwise