Instructions
Turn on the Xbox 360 that you used to recover your account. Do not sign in to an account. If you are automatically signed in, press the Xbox "Guide" button and press "X" to sign out.
Go to the "My Xbox" section of the main Dashboard and open "System Settings." Open the "Memory" section and open the device that you used to store your recovered Gamertag.
Open the "Gamer Profiles" section. Highlight your Gamertag and press "A" to show options.
Select "Delete." Choose "Delete Profile Only" to delete your account credentials from the console. Choose "Delete Profile and Items" to delete your account and all associated data -- this includes saved games and Achievements. Any Achievements you obtained while online were synced with the Xbox Live servers, so deleting them from the console will not erase them entirely. They will show up the next time you sign in to Xbox Live using your Gamertag.