Alright, I understand the issue.
Since you are not using any other features in the JFBCLogin module, I would recommend creating a new Custom HTML module. Put it in the same location as the JFBCLogin module. In the text, simply put:
{ JFBCLogin}
Without any spaces. When displayed on the page, it will show the Facebook Connect button only to guests.
If you want to use the JFBCLogin module, you'll need to modify the following file:
/modules/mod_jfbclogin/tmpl/default.php
Delete line 121 and 122:
<div class="fb_connect_user"><?php echo JText::_('Connect User'); ?></div>
<fb:login-button v="2" onlogin="javascript:jfbc.login.login_button_click();"><?php echo JText::_('MAP BUTTON'); ?></fb:login-button>
Hope this helps. Good luck!