How do I move a Time Machine backup from an external hard drive to the trash?

I backed up my MacBook Pro laptop to the wrong external hard drive by mistake. I have since backed the laptop up to a different external hard drive that is dedicated only to backups. I need more space on the first hard drive and do not need the old back-up that is taking up a lot of space on it. I tried to delete the back up, but even when I unlock the file I cannot change the permissions to allow me to trash it. Can you help?