Ed,
Yes, this is a bug in the current version of JFBConnect that has been fixed in the next release. You can make a quick code change below to fix it. Additionally, in general, we'd recommend making sure that the Error Reporting setting in your Joomla Configuration area is set to 'none'. This will hide any PHP warnings that come up from any extension.
Code change - /components/com_jfbconnect/libraries/profile.php, at around line 324, you'll see:
$path = JString::str_ireplace('http://' . $fbCdnUrl, '', $avatarUrl);
Replace that line with (change JString::str_ireplace to just str_replace):
$path = str_replace('http://' . $fbCdnUrl, '', $avatarUrl);
This affects the avatar importing functionality, and should have no effect on your site.. but obviously, test.
Sorry for the troubles, and good luck,
Alex