I use a child theme that allows me to have a functions.php file to add customizations to, but you could do so in your main theme functions.php file.
You should be able to just added the code,
// remove "Sale" icon from product images
remove_action( 'woocommerce_before_shop_loop_item_title', 'woocommerce_show_product_loop_sale_flash', 10 );
to the the end of the functions.php file, before the last ?> if it has one.