Delete or Disable Alternate Email

Hi, I want to disable or delete an alternate apple id email that is associated with my primary Apple ID account. People are sending email to that address believing that I am receiving the email, but I am not (and don't want to as I already have a primary gmail email account). Can I somehow disable or delete this secondary email address so that people get a bounce-back or something if they try to send to it? When I go to the Manage My ID section of the apple website, it just says this:

Alternate Apple ID

xxx@me.com

You can use your Apple ID or your Alternate Apple ID to access everything you do with Apple.

But it does not give me an option to delete. Any help appreciated!