Gary doesn't want his email to get deleted from his computer when he deletes it off his phone. Leo says that PoP3 deletes mail on the webmail's server after it gets downloaded to the email client, while IMAP shares the same view as the webmail and keeps it. So any changes he makes from one device would echo to the server and vice versa. So it may just be the way it is set up.
Leo suggests not using the Verizon email program, and use the stock email program that comes on the phone instead. Also, Gary should set up a gmail account and let it go get his email from Verizon.