How to update Time Machine's recovery partition? The backup disk used by Time Machine has a recovery partition you can boot from.

Since I started using Time Machine with OS X Snow Leopard, the recovery disk is a Snow Leopard recovery disk, and will only Snow Leopard.

How can I update the disk to be a Mavericks recovery disk?
The hard way: Wipe the backup drive. Set up Time Machine again to backup to this drive. Wait for the backup to complete - and find a Mavericks recovery partition on it.