Deleting Aperture trash

Recently I obtained a new iMac and had to move my pictures to an external disc. I have encountered a problem with deleting Aperture trash from that disc. When I delete the trash I get a message that files cannot be moved to System Trash because I "don't have access to the System Trash on the original files' volume." I researched the issue and understand that the problem lies with permissions on the external drive (a Seagate 3TB). I tried repairing permissions but no success. I have also accessed the Seagate disc drive information and did what I could to extend read and write privileges but, again, no luck. After checking the "Ignore ownership on this volume" option on the Info pane I did obtain a small measure of success in that the message about not having access to the "original files' volume" did not appear.

When I empty the Aperture trash the files vanish. They do not appear in the main system trash nor can I uncover any trash file on the Seagate. When I go to import new photos the pictures that I deleted will show up as being on the Aliceimac.local device. I assume this is the Seagate?

Anyway, I'm confused as to how I can get these deleted files out of my Seagate and I also want to assure that they get permanently deleted from my original files.

Thanks.