If you take look at the wickett-twitter-widget.php and go to line 104, you will see this:
104: echo "{$before_widget}{$before_title}<a href='//twitter.com/{$account}" ) . "'>" . esc_html($title) ."</a> {$after_title}";
Now if you delete these parts:
<a href='" . esc_url( "https://twitter.com/{$account}" ) . "'>
</a>
the url from the link will be removed.
To include code below each tweet go to line 175.