You sound like a neighbor I had in California.
The roots of my tree was growing into their lawn. He cut it off and threw it over the fence. I threw it back and that went back and forth for about 4 throws. The last time I threw it back he threw it in the garbage. The reason why I decided to throw it back was he has always been unreasonable. They were very high strung people and I was not going to let him do this. Also, he has a peach tree that was always heavy with peaches. I always found more rotten peaches on my side of the fence than was hanging on the tree to drop on my side.
I don't go knocking on the elderly ladies house behind me saying your tree branches are growing over my fence. My husband cuts them off especially when they are on the fence. After he cuts and trims the trees he put them out for the garbage collector.
Just Throw it away.
