Now when you've backed up iPhone to portable hard drive, run a test to see whether iTunes is really backing up from the new location:
Connect your iPhone or iPad.
Launch iTunes or find your device via Finder.
Select Back Up Now.
With the backup completed, open the iOS_backup folder on the external drive.
Check the date and time of the last backup — it should coincide with your recent activity.
Only after the test proves successful can you delete your old backups.