When I hit Gigi with my net she doesn't do anything. I have hit her 10 times in a row and she just keeps walking. But if I do this to any other villager they either get angry or upset after three hits...?
Also, I really want to get rid of Gigi, and Sylvia... and Knox and Goose. So, does anyone know the best way to do it? Do I just ignore them (I haven't spoken to Gigi all day), or do I push them around, make them fall in holes or...? Hmm...
You get the hammer on the island, it shows up from time to time. When I used it, my villagers got upset, it was a bit of a shame actually! "I never thought a friend would do something like this to me". Oops...
If you're on Wi-Fi, your villagers will not get angry with you if you push them, hit them, etc.
I believe it was implemented to prevent people from successfully bothering another person's villager.