The yellow leaved version of Catalpa bignonioides is slow growing - after 25 years, it should be between 8-12 metres high with a spread of 8 metres or more. Even so, 9 feet from your house foundations is too close.

Catalpa can also be cut back hard in the spring to produce shrub like, smaller plants but with huge leaves....maybe that's their intention.

I would worry if it was me though. There isn't anything like room to accommodate its eventual spread if they don't intend to keep cutting it back. Does your neighbour know how big they grow?

Thank you all. You have been very helpful. I think I had better point out your comments to my neighbour.