Release group SYNDiCATE has made available Nintendo Wii Backup Disc v1.31 today. According to the included NFO file: "This is the originally correctly signed version of Nintendo's Backup disc, which was left in a console after repairs." Unpacked, the image's size weighs in at 600 MB (629,145,600 bytes) and the release name is Wii_Backup_Disc_v1.31_USA_READNFO_WII-SYNDiCATE.
Download: Wii Backup Disc v1.31 / Wii Backup Disc v1.31 [Mirror] / Wii Backup Disc v1.31 [Mirror]
To quote from WiiBrew (linked above): The "Wii Backup Disc" is a service disc apparently used inside Official Nintendo Repair shops to transfer personal data like savegames and console settings between Wiis as part of a repair.
It's not entirely clear what it does; something it does *not* do -- even though it appears it might -- is allow VC games to be transferred between consoles. Instead, the user is told to redownload the games from the Wii Store (for free).
Note: "Change WiiId" is mostly useless. WiiId is only used as your "Wii Number" that you give to your friends so they can send you Wii Mail. When you pick it, it assigns you a new random ID.
It also doesn't boot on full bricked Wiis and it's unlikely that it repairs half bricked Wiis since delete all only deletes savegames/settings and not any VC content (Weather/News/Games..) or the firmware. More PlayStation 3 News...