It is coming back because the setup for the Library Manager (including any additional Libraries added, but not active) are included in the Settings portion of the Library Backup.
You should be able to delete the Library via the
Library Manager. Please note that you cannot delete the currently active Library (which it should not be because you said it is broken). Select the Library itself within the Library Manager section of the tree, and choose Delete. Or, if that doesn't work, try selecting the Playing From <CURRENT LIBRARY> item itself (the top of the Library Manager), click the Delete Library button, and then select the blank one from the pop-over list.
If none of this works, you could also make a backup and the edit the settings file manually, and then restore the backup (make and save an unedited version so that if you bork this up, you can undo it). To do this, make a Library Backup, and then open (or unzip) the Zip file. Inside there is a folder called
Settings and then a file called
User Settings.ini. Open this file up in a decent text editor (I'd recommend Notepad++) and you can edit or modify the settings that will be restored.
The stored list of Libraries is found in the
Properties\\Libraries key. Each available Library has an associated entry here. The
DisplayName property shows the names you gave them in the Library Manager. You can remove an entire key here to remove the Library entirely from MC's setup.
Save the file, rezip the package if needed, and then restore it.