I don't particularly trust the space 'used' by an indirect listing by an app. Disk Utility may give you a more accurate value, or even a Finder display.
I'm assuming you used TimeMachine to designate what files to delete and
not simply deleting from Finder? I'm not sure what "control-erase" means.
I've deleted stuff from TM backups many months ago, but
ONLY from within TM. You are then offered the option of deleting all instances of the file/folder or just the one you have selected for any particular date. But I've never bothered to see what space might have been restored since my deletions were rather small. Note that a file is usually only stored in one place in TM (the first instance). All other references are similar to an alias. So you won't have actual duplicates of the 10GBs worth of files in the backup.
Within TM !!! as I stated.