American grey squirrels are a pest in England. They have killed most of our native red squirrels with para-pox virus, As grey squirrels are twice a s big as our vegetarian red squirrels, they also kill them and grey squirrels are carnivorous. They eat bird eggs and anything else they can get. In the U.K. They are considered an Horticultural and Agricultural pest! It is illegal to feed them as some people do in parks.
However Goshawks thankfully eat them, and it is legal to shoot them in the UK.
Regards.
Neil.