Recovering a few files (or even most of them) in a backup does you no good. It's no longer a backup. I wouldn't even attempt to recover from this problem. Wipe the drive, let TM start backing up anew to it, and chalk this up as a lesson learned.
It's easy to keep Time Machine itself backed up. Just start a TM backup on a different disk, and occasionally swap the drives. The initial backup will still take a long time, but when you rotate back in a previous TM backup, TM only needs to copy what's new for that drive. If you can keep them both attached, TM will even do the rotation for you.
I started doing that (keeping multiple TM backups) after losing a TM drive to hardware failure. Then I discovered it's really convenient for off-site backup. TM can bring a backup disk up to date much faster than the other backup solutions (SuperDuper, CarbonCopyCloner) can.