File Vault 2 w/ Time Machine Restore

I just purchased a new laptop and decided to transfer all my information from the old computer by simply doing a restore from time machine backup on the new machine. It pretty much worked flawlessly.

That said, when I went to turn on FileVault 2 on the new computer, it said that a recovery key had already been set by school, employer, etc.

Does anyone know if the recovery key stays with a time machine backup? I am hoping that the old recovery key will work with the new computer, but it is making me a little nervous . . .