Q: How do you delete a backup that was created with an ID that is no longer used? For instance. I originally purchased an iPad with my personal email address ID, then set it up with an iCloud email address ID and later did a factory restore and set it up with my personal email address ID. Is the backup done under the iCloud email address ID stranded?
A: The backup won’t be “stranded” per se, but you will need to log in from an iOS device or Mac using the old Apple ID in order to see it so that you can then delete it. Ideally, you would normally do this before switching over to the new Apple ID, but if you’ve forgotten to do so, it’s not overly complicated to switch back.
Note that there’s probably no harm at all in leaving your old iCloud backup with the other iCloud account, but if you’re concerned about leaving personal information lying around in the cloud and want to remove it for privacy reasons, you can do so simply by switching back to the old account.
On an iOS device, simply go into the Settings app, select iCloud, and then scroll down and DELETE your iCloud account. Don’t worry as this isn’t as bad as it sounds—all of your data is already stored in iCloud, so all you’re doing is deleting the local copies from your device. When prompted, you can choose to keep or delete information such as contacts and calendars; whether you choose to keep them or not, they’ll simply be resented when you later switch back to your proper iCloud account. Usually selecting the “Keep” option is a bit simpler as there’s no point in deleting this information.
Once you’ve done this, log into your old iCloud account as you normally would, and be sure to turn all of the options OFF, as you don’t want to resync your data with the old account. You can then tap on the Storage & Backup option and select Manage Storage to see your old backup(s) that are stored in that account.
Tap on the backup to see more detailed information and tap the “Delete Backup” button to remove it from the iCloud account.
Once you’ve done this, you can then remove the iCloud account in the same manner as you did for your primary account, and log back in to your proper iCloud account, being sure to set your sync options as you had them before.
You can also do this from a computer running Mac OS X Lion or Mountain Lion by going into the iCloud section in System Preferences, signing into the old iCloud account and choosing the “Manage Storage” option. If you’re concerned about removing iCloud data from your Mac, you can also do this by setting up an additional user account in OS X, switching to that account, and logging into iCloud from there—each OS X user gets their own iCloud settings.