Time Machine Clean-up

Somebody please help me: I deleted my old backups from my time-machine. When I unplug the external drive where the backups are located, there is nothing in my trash can. But as soon as I plug it and access the files in the external drive, everything I deleted from the back-up comes back into the trash can. How do I solve this problem. I want those old files gone for good and my external drive cleaned out.