Display list of most recent grandchild (third tier) pages

The only (easy) way this can be done is to query all special, calculate their depth, and then build a new stack of 3-level deep:

$grandkids = array();
$specials  = get_posts(
    array(
        'posts_per_page' => -1,
        'order' => 'DESC',
    )
);

foreach ( $specials as $special ) {
    if ( count( get_post_ancestors( $special ) ) === 2 ) {
        $grandkids[] = $special;

        if ( count( $grandkids ) === 3 )
            break;
    }
}

foreach ( $grandkids as $post ) {
    setup_postdata( $post );

    // Do your stuff
}