Removing comma from ‘entry-date’ in Twenty-Sixteen theme

get_the_date and get_the_modified_date use the date_format option set on the Settings -> General screen. Changing your date format there should change the date formatting returned by these functions without having to change TwentySixteen.

You can also use the filters of the same names to conditionally filter the dates depending on conditions. For example, show a different date format on pages:

add_filter('get_the_date','custom_get_the_date',10,3);
function custom_get_the_date($the_date, $d, $post) {
    if (is_page()) { // date display on pages
        $d = 'jS M Y'; // custom date format, see PHP date function
        $post = get_post($post); if (!$post) {return $the_date;}
        $the_date = mysql2date( $d, $post->post_date);
    }
    return $the_date;
}

add_filter('get_the_modified_date','custom_get_the_modified_date',10,2);
function custom_get_the_modified_date($the_time, $d) {
    if (is_page()) {
        $d = 'jS M Y'; // custom date format, see PHP date function
        $the_time = get_post_modified_time($d, null, null, true);
    }
    return $the_time;
}