However,
"The height of hedges, bushes and trees that serve as natural screening are not regulated under the Fence By-law. They should however be maintained so as not to create a hazard, in accordance with other relevant by-laws."
For sure it will be bad for the house! Surprised and felt strange they were not accept your idea!
Try to explain nicely again to them. The tree is going so big now, maybe they'll change mind to take it off? Tell them if it damage the house, their house value could be dropped a lots!