I assume you already make use of auth token & session idle timeout (in the user or COS > advanced tab > timeout policy at the bottom)
(I take it you couldn't get management to understand the difference even.)
To change just the text of "remember me on this computer":
1. cd /opt/zimbra/tomcat/webapps/zimbra/WEB-INF/classes/msg (it will be in jetty in 5.0)
2. vi ZmMsg.properties and search for 'rememberMe'
3. vi ZhMsg.properties (for the html client)
4. tomcat stop/start
Now the checkbox will still be there-so you could get creative on your wording

Or if you want to make things interesting-set the auth token and session idle timout as low as minutes or seconds for the individual user that complained-then see how fast the complaint stops when they have to login 20 times a day...
To remove check box all together:
1. cd /opt/zimbra/tomcat/webapps/zimbra/
js (jetty instead of tomcat in 5.0)
2. gzip -d -S .zgz Ajax_all.
js.zgz
3. Search for the following setting: _12e0.showRememberMeCheckbox=true;
4. Change to _12e0.showRememberMeCheckbox=false;
5. Save this File
6. gzip -S .zgz Ajax_all.
js
7. cd /opt/zimbra/tomcat/webapps/zimbra/WEB-INF/classes/msg (jetty instead of tomcat in 5.0)
8. vi ZmMsg.properties and search for 'rememberMe' comment this out with a # sign
9. vi ZhMsg.properties (for the html client) again comment out 'rememberMe'
10. tomcat stop/start or a full zmcontrol stop/start
Personally, I'm happy with session idle timeout of 1 day (so people can't leave themselves logged in overnight.) And auth token I usually set to 3 days.
Bugzilla request for the option to have the 'ogin 'remember me' checkbox show up or not via a setting in the admin console:
Bug 7958 - Disable "Remember me on this computer" on login screen
5.x directions:
To remove the 'Check Box' next to the 'Remember Me..' text. Edit the following file:
/opt/zimbra/jetty-6.1.5/webapps/zimbra/public/login.jsp
All you do is remove the below lines in red from the login.jsp file
<table width="100%">
<tr>
<td>
<input id="remember" value="1" type="checkbox" name="zrememberme" /></td>
<td class="zLoginCheckboxLabelContainer"><label for="remember"><fmt:message
key="rememberMe"/></label>
</td>
</tr>
</table>
To edit the 'Remember me....' text
/opt/zimbra/jetty/webapps/zimbra/WEB-INF/classes/messages/ZmMsg.properties
rememberMe = Remember me on this computer
(or comment out I suppose)
As a zimbra user, restart zimbra services:
su - zimbra
zmcontrol stop
zmcontrol start
or just zmmailboxdctl restart
Make sure you backup these files prior to making these changes. These changes may not survive an upgrade.