In order to activate the discount you need to use a minimum of one point to pay a portion of the purchase (don’t use more than one point as you usually get a poor value per point).
A great way to liquidate these discounts is buying third party gift cards sold by Amazon and reselling them on gift card trading platforms (Amazon gift cards do not trigger the discount). The gift cards currently reselling for a great value are BestBuy gift cards (thank you Matt).
Links to the deals
Check out these links to see which deal you are targeted for:
If you are not targeted for these offers then you can try to delete from your Amazon wallet the credit cards that are associated with the applicable points program. Wait a few hours then re-add the cards and try the links again.