You can use “post__not_in” Parameter. add your products id in array which you want to exclude.
$default = array(
'post_type' => 'product',
'post__not_in' => array(2024),
'orderby' => 'date',
'order' => 'DESC',
'post_status' => 'publish',
'showposts' => $numberposts
);
if( $category != '' ){
$term = get_term_by( 'slug', $category, 'product_cat' );
if( $term ) :
$term_name = $term->name;
endif;
$default['tax_query'] = array(
array(
'taxonomy' => 'product_cat',
'field' => 'slug',
'terms' => $category )
);
}
$list = new WP_Query( $default );