Mark discounted products in archive view

Hi,

I want to mark the products that a bulk discount with some badge. Is there any filter or action that can be used?

For example, on this page:
https://drinkandco.co.il/product-category/offers/page/3/

I use the woocommerce-smart-sale-badge addon to mark discounted products (the green circle), that plugins uses the woocommerce_sale_flash filter.

https://www.ads-software.com/plugins/woocommerce-bulk-discount/