Lesson learned building mybirth.day: the wall is yours, the memories on it aren't.
A wall is a page with your name where friends write and post photos. If you delete it, the memories stay. The dialog says it plainly: they are not all yours to delete. Each one still shows up in its author's My memories, marked "Not on a wall".
Same rule for links. Rename a wall and the link follows the new name, but the old one keeps working. Change your username and the old one is held for a while so nobody can grab it straight away.
What a friend wrote for you shouldn't vanish because you changed a setting.
mybirth.day/get
commit 5a4012c