iTunes sync does not delete songs

"Sync only checked songs and videos" was un-ticked.

When an iOS device is connected to iTunes, under the device's Summary tab, the Options section has a checkbox Named "Sync only checked songs and videos"; this option enforces the removal of music that is not set to sync if it has been synced to the device in the past.

Ticking the box and then syncing removed the offending album.

You can use DiskAid to safely access the iOS file system and delete Music/Data. The app costs $24.99, but you can get it for free on an educational license (have a .edu email ID).

Failing that, a restore might be the best option.

My bad, I didn't read the question properly.

This Apple forum post seems to suggest that songs downloaded by iTunes Match are not 'synced' in with iTunes, but via the iCloud. Maybe, these albums are from iTunes Match?

That post also details a way to delete all music from your iPhone (as opposed to deleting individual songs or albums):

You can do this on your iPhone by going to Settings > General > Usage. Wait a few seconds for the usage statistics to appear, then choose Music. Tap Edit and then the delete symbol next to “All Music”.

This will delete all the music from the phone. After this songs will still be visible (with clouds next to them). You can still play them from iTunes Match and they will be downloaded again; this will not remove them from iTunes Match.

: source

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