The Login area you're seeing is built into Joomla. You'll want to override that and basically remove the login form if you don't want it. To do so, copy:
/components/com_users/views/login/tmpl/default_login.php
to
/templates/<YOUR_TEMPLATE>/html/com_users/login/default_login.php (creating any folders that don't exist)
Then, edit that file and remove the form. While there, you can also add the {JFBCLogin} tag to add a Login With Facebook button and even give a description of why to login and how Facebook logins work, if you want.
Hope that helps!
Alex