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However, you cannot remove the email address from the list here like you could above.
Since this email address has to be associated with your Apple ID account, Apple will send an email to the address for security purposes.
When you get the email, tap on "Verify" to open up verification page in your web browser, then just submit your Apple ID password.
Once you get it, input the 6-digit code onto your i Phone's screen and you'll be set.
Shortly afterward, you'll see a popup asking to "Add '[email address]' for i Message and Face Time." If you select "Yes," you won't have to do anything else.
Note that you can enter in phone numbers here, but they don't seem to work for either Face Time or i Message, so we're not quite sure what adding a phone number will actually do.
Then, wait for Apple to send you a verification email to that email address.
However, if you verify them with Apple via the emails, they will show up back in the list afterward. This won't remove it entirely, but will just keep people from contacting you.
To remove it altogether, tap on the "i" (info) button next to it, then select "Remove This Email." After that, confirm by selecting "Remove Email Address." Just note that this only removes the email address from Face Time, and it will still be listed as an option for i Message and will still be associated with your Apple ID.
While this is all fairly easy to do, either on i OS 10 or i OS 11, it does seem a little more complicated than it needs to be.
Hopefully, Apple will streamline this process, which they seem to want to do by removing the ability to remove emails from either Face Time or i Message independently when you can just un-check them in those situations where you don't want to remove the email entirely.
More importantly, you can add any other email addresses you'd like to this list, so you never have to worry about a friend, family member, or coworker not being able to audio or video chat with you.