I live in South-East Northumberland in what's currently a red squirrel stronghold and am one of the appointed red squirrel wardens/rangers for my patch under the RSNE conservation partnership.
Sadly the area is being encroached on 2 sides by populations of grey squirrels who are seeking to expand their territories into that of the reds, so constant effort is needed by our volunteers to try and keep them at bay.
Yes the greys are cute and fluffy, but the sad reality is since their introduction to the UK they've resulted in a catastrophic decline in the native reds, so if we want any chance of preserving the little ginger buggers then the greys need to be controlled.
I take no pleasure in that fact but the reality is it's very much a case of choose one or the other. The greys are a recognised invasive species and even the government have legislated that it's illegal to re-release one in the event one is captured even accidentally, they must be destroyed instead.
As part of the conservation work I have a dozen or so monitoring stations to keep tabs on with feeders in place, the flip up lids have sticky pads underneath which capture hair samples and allow me to see what species are present at each station. When greys appear we use live-catch traps to catch them and they're disposed of humanely. They're very much edible either for human consumption or to feed to dogs/birds of prey etc.
I appreciate it may seem distasteful to some, but if anyone would care to read about the conservation work and why it genuinely is needed then there's some good info on the RSNE website (albeit not in the shiniest website format):
https://rsne.org