Perhaps you could explain to your plot neighbour that, having looked at the situation, it would be more awkward and expensive than you had thought to divert your fence to accommodate their greenhouse, but that if they would like help to move either the door or the greenhouse to a more suitable position on their plot, then you are more than willing to help them to relocate it.
This would seem to be a more sensible solution as the greenhouse is, after all, on their plot, and it really isn't your problem that whoever built it put it in an awkward position. Offering to help them rectify the problem should hopefully avoid any bad feelings.