You only fill in the GMI when the borrower is sitting in front of you completing the application and tells you they do not wish to provide.
Dropped off, whether it's handed to an LO or to non-mortgage personnel, is the same as a mail application. Same with fax, internet and email. We make a notation next to mail that the app was 'dropped off'.
Telephone you will mark what their responses are and leave it at that too.