How to hide extraneous "Sender" in simple header, when using aliasing?

I have an email on my domain forwarding to gMail. I then set up gMail to "Send Mail As" as my domain's addy. (And have marked that addy as the default sender, too.)

All works well. Except even in the simple headers (date/time/etc), an extra line shows up. It's "Sender" and has my gmail addy listed. This is a problem, because I was trying to keep my gMail address private.

I understand the need for that information to be disclosed in the full, detailed headers. But how can I prevent it from showing up to people who don't know anything about looking at full headers but can see it anyway?