mailman private archives showing in google search

I have a customer who just complained that his private moderated mailman email list, which has private archives available are showing up in google searches.

I took a look and he's right.

If I go to the index page of the mailman email list, I can't view the archive index unless I login as a valid user that is on the list or the administrator/moderator of the list.

However, if I search for one of the user's name which is on the list at google.com, I am able to find links to the archives of the list.

This only works because the user has a very unique name. His name doesn't show up too many places on the internet.

How can I fix this issue?

I double checked in the list admin to make sure that the list archives were PRIVATE.