How to mimic rename file operations on a backup disk having same layout?

I want to tidy my external harddrive. This harddrive is kept in sync with a backup via rsync. When I move/rename (and delete for convinience) files on the disk, it would be nice if those fast actions could also be performed on the backup drive analogical, so I don't have to rsync the corresponding files again. For tidying I like to use a GUI (i.e. pcmanfm). Are there any tools capable of this? //Edited b/c delete makes my point harder to see - I want to avoid rsync deleting renamed/moved files and copying them again to the new location. And I'd like to stick to the tidying process as I'm used to (move/rename and delete things in a file manager with graphical interface).