We can confirm this works as advertised.
After completing our stay, we received an email from booking.com asking us to claim our $40.
You simply need to provide them with a debit/credit card which they will then send $40 to as a refund (see image below).
Booking.com are running a promo where you can get $40 off a $80 hotel spend.
The $40 is credited back to your payment card after you complete your stay.
Strangely, there are no Terms and Conditions specifically for this promotion.
Only generic T&C found here.
Availability in 2018
When you click the GO TO DEAL button, there should be a promotional banner at the bottom of the page: