You may either remove that person from your Family Group or block them. Doing either of those actions should prevent that person from removing your profiles.
Also, you may view your Deleted Profiles list here: http://www.geni.com/list/deleted to undelete any profile you once managed which another user had removed.
Once a person has claimed their account, you cannot "uninvite" them. The report feature may be used to report activity which you find abusive, but not simply because they are removing profiles.