That error isn't coming from JFBConnect, as far as I can tell. The message itself of "JLIB_APPLICATION_ERROR_COMPONENT_NOT_LOADING" is a Joomla system error message. That's occurring because some component isn't loading, but I'm pretty confident that JFBConnect is loading.. it's some other extension on your site that isn't properly loading.
The reason the FB logo is there is because the container for the system messages has a class of #system-message > .message > ul and in your CSS file is the following styles:
#system-message > .message > ul {
background-color: #5f78ae;
background-image: url("http://..../images/facebook/fb_icon.jpg");
}That CSS is saying to wrap any system error messages in a look like a Facebook Login button. That CSS is in the following file:
templates/indielife/XTC/css.php?id=7&file=template
I have *no* idea why the CSS is declared like that, but that's what is making you think it's coming from JFBConnect.
I hope that helps explain and narrow things down for you. If you have any more issues that you can narrow down to JFBConnect, please let us know what they are, and we'll gladly investigate further.
Thanks,
Alex