How to get rid of old "backup" folders cluttering my Sync folder list?

[yoshm]

I was backing up folders from my old phone to my home computer. 

 

Now I've switched to a new phone. I want to keep the backups from the old phone, but obviously don't need them to sync/backup anymore. I disconnected them, but they still clutter my Sync interface with "dashed" folders. When I try to "Remove" it warns me that it will delete the folder from all my sync'ed devices. 

 

Frankly, I don't understand what that means. Is it going to delete my backups? How can I simply say - "Leave everything alone, just take this folder off your list of things because I don't need you to worry about it anymore" ? 

 

Thanks,
yosh