That's awful!
Grey squirrels are a pest here too, and people feed them, which obviously makes it a lot worse. My dogs love to chase them though!
On the subject of invasive/unwelcome species, I want to have a word with whoever introduced coyotes in vast numbers to the Northeastern US... they have become a huge pest, not just a pest but a *menace*... they will attack people and there have even been a couple of deaths recently, they eat pets and livestock, and they are not afraid of humans at all, and can adapt to living in developed areas. They are smaller, but more aggressive, than wolves, although they often hybridize with wolves, and you can imagine how that goes.
Coyotes are such a problem here that hikers in certain areas are actually encouraged to carry sticks or even weapons.
They are also bad for the fox population here, since they seem to be a deterrent for them, and red foxes are becoming scarce here due to habitat destruction. Foxes are timid and relatively harmless due to their size (a red fox is smaller than a Corgi-sized dog, they're usually about 10-15lbs.) Foxes are also opportunistic predators and are naturally afraid of humans. Coyotes don't have that same fear and are getting to be much more confrontational.
Coyotes are the one species of canine that I really don't care for. If one ends up on my property and attempts to attack or threaten my dogs, it will be having a bad time.