OP,
It's hideous.
YANBU.
The tree surgeon butchered the tree and now you have been left with the eyesore.
They may have stuck it up whilst the house was empty.
It's the type of thing opportunistic people do.
It is surprising that they didn't monitor what the tree guy was doing considering what he's left them with.
Given the different dimensions of the garden, it's interesting and telling that they built it as far away from their house so the noise is on top of you.
I absolutely believe it would put a buyer off.
I would follow @DeRigueurMortis excellent advice.
With loads of photos.
Fyi bamboo in large plastic pots could cover this eyesore at THEIR cost.
Lime trees are another expensive solution.
The pots are crucial to stop the bamboo going mad, it spreads quickly.
You can buy bamboo that is 6 or 7ft, but they are obviously expensive.
When the treehouse had coverage from the tree it was acceptable but this eyesore is awful and horribly intrusive.
They remove it or they come up with something that restores your privacy.
Get this sorted before the spring.
This will ruin your summer.
From those photos it's easy to see how it was missed.
But I really bet it isn't up long.