Alex,
The following bug report is the one to follow from Facebook about this issue. If you're using the 'full' Invite view, there is a workaround. If you're using the Condensed version, there isn't currently one and you'll need to wait for a fix from Facebook:
developers.facebook.com/bugs/28816869120...0977928d048361972345
To fix the full version, edit the /modules/mod_jfbcinvite/tmpl/default.php file. Around line 52, you'll see:
<fb:multi-friend-selector
On the next line add the "import_external_friends" setting as shown below (with the above line as well):
<fb:multi-friend-selector
import_external_friends="0"
Hope that helps, and thanks for reporting this. We're planning a complete revamp of the Invitation logic to move to an improved system. Shooting to replace the currently available system in 4.1 (roughly December).
Alex