Could a 'damaged' TimeMachine backup still be of any use? I've got a Synology NAS here and a few months ago I sadly got the message, something like


  Time Machine backup is corrupt and therefor has to start a new backup.


However, as my NAS is starting to get more and more filled, I'm seeking to kill some data. I found this old backup which is about 650GB of size. 

And my only question is: Can it be of any use or should I just remove it completely?

If you ask "But by starting a new backup, the old one gets deleted. Why do you still have it?" That's because it ended up in the Trash, instead of permanently deleted.
The nature of Time Machine is such that it isn't an archival backup, as files deleted from the source drive will eventually disappear from the Time Machine backup set.1 If you have no other backup however, it might come in handy.

If the sparsebundle can be repaired, you'd be able to extract files from it. Following the instructions in the first green box of http://pondini.org/TM/A5b.html might let you access the backup set.

If you do gain access to it, you can use the Time Machine interface2 to remove all backups of folders you don't care about, but it might be tricky to cause the sparsebundle to take up less disk space.3


1 See the text starting with "Time Machine keeps" in https://support.apple.com/HT201250
2 "Remove a backed-up item from your backup disk" - https://support.apple.com/kb/PH11241
3 "Changing the size {…} of a sparse bundle" - http://pondini.org/TM/A8.html