From your mailbox, click on the settings icon and select Mail.




From the Preferences for Mail page, select Deleting and Moving Messages option.

   


Check the box for the “Move deleted messages to your Trash mailbox instead of marking them as deleted in the current mailbox” option and click Save.



Go back to your Mailbox and check all the emails you want to delete (including the greyed out), click Delete, and it will move all deleted items to your trash folder.