Hello! As far as I know, it is not possible to delete a family tree permanently - you can only "Remove" it, but it is always able to restore a removed tree. If you are worried about privacy issues, you can delete each person on the tree individually (which, I think, can't be reverted), but that can be a long and strenuous process depending on the number of people on the tree, and still "keeps" the tree on your profile.
