Hi,
Yes ; there is nested P but there is one single parent : "hikashop_cart_product_custom_item_fields".
You can take a look into the view "product / cart" (which is the view which generate the module content) ; you will see that code
if(!empty($html)){
echo '<p class="hikashop_cart_product_custom_item_fields">'.$html.'</p>';
}
$html is the variable which contain the content of the item custom field for the item. If you remove/comment these 3 lines, the item custom won't be displayed anymore in the page.
Regards,