How do I remove mail folders from "On My Mac?"

Hi

I believe my problem is related to Mavericks. 10.9.2. Using Apple Mail and a Gmail account.

I am repeatedly being asked to re enter a password for a Gmail account, so I deleted the Gmail account on all Apple devices (at least I think I did).

So I continue to be hassled for a password to this Gmail account when I open Mail, even though the Gmail account does not appear in my System Settings or under Accounts in Mail.

I do see folders for this same Gmail account in Mail, under the heading "On My Mac."

Do I need to delete these folders as well? If so, how?

Ultimately I would like to reinstall the Gmail account. But I really believe I need to compeltely delete it from my Mac, so Mail will accept the stored password. Tell me if I am wrong.

Thanks

AS