your neighbour sounds like a bit of a grumpy old dude - just rise above it and in spring merrily trim the vines on their side with a beaming smile. whistle while you do it, too. grumpy people hate that.

I would remove the vines though, as advised above. they will just get bigger, as will the problem! there must be plenty of pretty non-invasive climbers in america, you could look on it as an opportunity to experiment...

bob