With a diagnostic OS, you’ll likely find yourself mounting many hard drives – either while NetBooted, or booted from an external hard drive. If Time Machine is not enabled, it will offer to backup to any reasonably-sized hard drive connected to your machine.
To disable this, run this command in the Terminal:
defaults write com.apple.TimeMachine DoNotOfferNewDisksForBackup -bool YES
This will prevent the Time Machine prompts from appearing.
Tested with: 10.5, 10.6, 10.7, 10.8, 10.9, 10.10