For your gift not to show in your new product listing on your homepage go to Catalog/includes/modules/new_products.php and find

$new_products_query = tep_db_query("select p.products_id, p.products_image, p.products_tax_class_id, if(s.status, s.specials_new_products_price, p.products_price) as products_price from " . TABLE_PRODUCTS . " p left join " . TABLE_SPECIALS . " s on p.products_id = s.products_id where products_status = '1' order by p.products_date_added desc limit " . MAX_DISPLAY_NEW_PRODUCTS);

change this to

$new_products_query = tep_db_query("select p.products_carrot, p.products_id, p.products_image, p.products_tax_class_id, if(s.status, s.specials_new_products_price, p.products_price) as products_price from " . TABLE_PRODUCTS . " p left join " . TABLE_SPECIALS . " s on p.products_id = s.products_id where p.products_carrot = '0' and products_status = '1' order by p.products_date_added desc limit " . MAX_DISPLAY_NEW_PRODUCTS);

I have included the new.products.php file

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