I live in the middle of a shoot. I have never had any problems from the gamekeeper. I have seen birds fall while I'm flying back to my LZ. I just hope some idiot with a gun doesn't take a pot shot at me.
Pheasants take no notice of the helicopter unless you fly over them. Then they run away. I keep in a high hover taxi when there are birds around. Never really a problem.
Edit: By the way, When theres a shoot on the place is crawling with police, shooters,'Antis' and occasionally reporters. Best remain impartial on the morals of shooting. Thats an issue you and your helicopter really don't want to be mixed up in. Your airmanship has to be pretty good too so you dont wind any of the interested parties up. I have landed to find nine police officers at my gate watching. (including 2 on horses!!)
'Oh s***' thought I. It turned out they were just bored and they were very friendly fortunately. No Anti's about that day.