Edit the excerpt before it is shown

Well, I found it:

    function get_the_excerpt_filter( $excerpt ) {
        $wordToRemove = "Introduction";
        $len = strlen($wordToRemove);

        if(substr($excerpt, 0, $len) == $wordToRemove){
            $excerpt = trim(substr($excerpt, $len));
        }

        return $excerpt;
    }
    add_filter( 'get_the_excerpt', 'get_the_excerpt_filter' );

Hope this helps someone else.