When you reply via email, simply delete all of the information after what you type.

You have your email settings set such that your reply INCLUDES the email to which you are replying in your reply. The means that your email address will be in the reply.

Kind of like when you get forwarded emails from friends which are pages and pages long which ALSO include the email address from anyone who has ever received the email.

Just delete the email tacked onto the end and your replies will no longer have to be moderated.