We don't have an option to do that, but it's a good idea. I just did some research into the Twitter documentation and there does look to be an option to show/hide re-tweets. If you're interested in implementing a small code change and testing, we'd love to hear your feedback.
To make the change, edit the /components/com_jfbconnect/libraries/providers/twitter/channel/stream.php file. Around line 53, you'll see:
$params['oauth_token'] = $accessToken->key;
Directly below that, add the following:
$params['include_rts'] = false;
While testing, please go into the JFBConnect -> Configuration area and set Debug Mode to "Yes". That will disable all caching so that the feed will update on every page load. If you don't do that, then the feed won't update right away.
Please let us know how that goes. If it works how you expect, I could definitely see adding this as an option in a future release.
Thanks!
Alex
Show only own tweets
