Shopify recently introduced the ability to combine multiple discounts on one order. The limitation of this is that one line item (product) in the cart can only trigger or use one discount. As a result, Shopify now marks any line item using a discount (either triggering or using one) - this has led to some themes built before this update to show discount labels beside products that are not actually getting discount, they are simply triggering a discount.
We have instructions here to help you hide these labels: