Even with Norton installed, getting rid of a Norton 360 backup file can be a pain. Once you remove Norton, I found little helpful guidance on how to do so. Here's how I did it:

To remove an N360_Backup directory created with the most recent versions of Norton Lifelock:

  1. Right-click on the N360_backup folder and select Properties.
  2. Select the Security tab
  3. Click the Advanced tab
  4. Click on Continue
  5. Click on the Deny permission and then click Remove
  6. Click on Add
  7. Click on Select a Principal
  8. Enter your username into the box and click Check Names to ensure it is correct
  9. Click OK
  10. Click Full Control
  11. Click OK
  12. Click on "Replace all child object permission entries with inheritable permission entries from this object"
  13. Click OK. then Yes
  14. Wait; it may take a long time for these permissions to update.
  15. The N360_BACKUP folder can now be deleted.

If your N360_Backup folder was created with an older version of Norton, this video may better indicate how to proceed: