You just have to change inc/front-popular.inc by this lines for the $popular part :
<?php
$popular = new WP_Query( array(
'post_type' => array( 'post' ),
'showposts' => 3,
'ignore_sticky_posts' => true,
'orderby' => 'comment_count',
'order' => 'dsc',
'date_query' => array(
array(
'after' => '1 week ago',
),
),
) );
?>
And… FRESH CONTENT IS HERE NOW !