Each family member can delete a post (message, photo, event, check-in, place, task, and contact) that he has published. A family member cannot delete a post of another member if he’s not an administrator member. A removed post is permanently deleted from the FamilyWall service.
A family member can delete a conversation thread. This thread is removed from his inbox but is still visible on other members’ inboxes (other recipients of the message). If another recipient answers to the thread, the member who deleted the thread will receive the answer. However, he’ll not see the deleted part of the thread.