Ah. Actually, I just re-read the post and realized that you were talking about the Login Module, not the Invite module. CMS Market is still using version 1.0 of JFBConnect (which we don't recommend you move too). However, the 1.0 module is very similar to the 2.0, and you should be able to disable many of the options using the module parameters. To get it to be that minimalistic though, you would need to edit the /modules/mod_jfbclogin/tmpl/default.php file to remove a bit of code.
The post below has an example of a customization to the login module that may help get you started/give you ideas:
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