I think you can politely ask sometimes; but I don’t see a problem with tall trees. They simply belong and are also useful. Here, many neighbors have very tall trees and that’s a good thing (even just as a privacy screen and shade provider). If there is damage, there are insurances and otherwise... big trees are usually old and have been standing for a long time. You don’t always have to cut everything down just because it could theoretically happen that the tree falls during a storm (and all ideas on how to damage a tree so that it dies or has to be cut down are simply illegal, and rightly so, such actions are punishable with hefty fines!). But as I said, talking helps. You will surely meet the woman sometime. She will move in eventually. And if you know who provides her with photos, then try to send a message to the woman through that person?
Trees provide shade, ensure a better climate, offer food and shelter to animals; rather enjoy them, because old trees are beautiful and worth protecting.