Hi eyeojo,
I think I'm hearing you just want your backup on your external drive only and no longer want iTunes info saved on your HD?
If so, you would delete the backup file in your iTunes media folder on your Mac (of course, make sure you have backed up items on the ext HD first, for sure). Don't go into your library specifically....you could cut out important info that helps run other processes & really get yourself into a bind.
Then, upon a new backup from your phone, you need to change the location you save to straight away before any backing up or syncing.
When I changed mine to backup to my external HD, I recall having to quickly stop the automatic syncing that began while connecting my device, in iTunes. Only then, would it just go to my external. The syncing app is built in, so sure, there's a possibility that the new items could get saved. Just go to the folder and delete the synced or backed up items. My synced items never actually saved on my Mac however-some did temporarily but disappeared after I'd restart my Mac; it is only upon backing up. There's definitely a significant difference between the two. If unsure as to what got saved where possibly, unplug your device after allowing your phone or another device to sync. IF you did not elect to backup automatically, etc, that synced info should not be on the drive. If it is and it appears to be permanent vs a temp file until restart for example, check your settings in iTunes for syncing and backing up. Also, check your settings for Time Machine and/or other processes you use to backup. Make sure they're on point and as you prefer.
All the best. You got this ;-)