Go to Integrations > Channel Manager > International > Booking.com

Scroll to the bottom of this page. There you will see several options. One of them is Send discounted rates.

Change the setting in the drop-down to Yes. Then scroll to the bottom of the page and click Save.
When this option is set to NO, the discounts are still applied to your website and/or other channels, but they will not apply to Booking.com.

In order to forward the changed prices to Booking.com, use the Send all data function in the channel manager.
It can be found below the last property listed on the page.