the way we did it was to edit the file located in /opt/zimbra/jetty/webapps/zimbra/public/login.jsp
I will be working on some changes tonight and will get you the exact location in that file once I take a look at it again. I wanted to give you the file location now however in-case you have time to figure it out before I post back.
There also may be a way to remove it in the "Messages" file - which I'll also find tonight when working on this.
The line we removed in the login.jsp file was:
<div class="offline"><fmt:message key="switchToOfflineClientEx"/></div>
We make a script that we run after ever update to make all our modifications for us. This way we don't have to manually edit these things out everytime we update/upgrade.. Zimbra update/upgrade replaces these files back to their new format.