Hi, I had the same thought- maybe the beat up goose is really a gander, but I turned her over and she looked female, where HE definitely has a male organ. Also, she looks Very feminine- much smaller ccompared to him. My neighbor who used to have a flock of geese came over and said thought she was a female, too.
I decided to put the bonded pair out of the pen and put the injured goose in with my three friendly female ducks. When I carried my injured goose back there to separate everyone out, he came after her angrily, so maybe he just is a one woman guy. He hurt the drake that I used to have. So far he seemed to still like the three ducks, and but I feel better about keeping them apart now, because they could be next! My yard (an acre) has a 6 foot fence, so we don't have dogs getting in, but the pair is just going to be out in the yard for a while until I can make another secure pen, so I hope it will be okay. I got them a deeper pool and put a nest box near it for her. I''m glad we haven't started planting the garden yet!! So far he has not been aggressive towards us, and he was a sweetie uuntil breeding season began, so as long as he can be happy with his woman he can stay. He likes singing, by the way, don't ask me how I know.
thanks everyone for your replies and advice- oh and they are American buff.