Jeffrey has his email set to IMAP and he has thousands of emails on his phone. How can he delete them? Leo says if he goes into his settings, he can have them deleted/expunged from the server. That's in the client settings on his phone, but it's not on by default. So if he deletes them from his computer, which is easier, it should delete them from Gmail.
As for his phone, he doesn't really have a copy of the email there. it's just a window to the cached copy on the internet. So if he refreshes the phone, the email should disappear. The issue is that Jeffrey thinks he's using IMAP, but he may be using POP3. It's not set that way by default though — Gmail uses IMAP.