Follow the procedures given here to remove old unread emails on ur gmail account.
It’s easy. Sign in, go to the search box, type in:inbox is:unread to get all unread messages, select all of them and then click on delete (which you can find by clicking on the ‘more’ option). Anyhow, I’d say do a quick look through all your unread emails so that you don’t accidentally delete any important email that you haven’t noticed or read. However, as long as the deleted emails remain in the trash folder (where it remains for 30 days) you can recover any of them, but yes, only as long as they are in the trash folder!