I'm not aware of bookit. com, but if it's like expedia, I don't think you can get points. I copied the piece below from the terms and conditions page on marriott.com
I think that it is down to the hotel whether to credit you or not. When I have used a third party to book, I just present my MR card at check-in and they normally just add my Rewards number. However, if it is a bargain basement rate, they may decline. As PP states, the T&Cs do impose limitations but it's always worth a try.
Thanks, painedplatinum is correct - rooms booked through third party online retailers are not eligible for Points or
Elite night credit.
Check out the Terms and Conditions for Vacations by Marriott. There is the reality that you do not get elite night credit or points for those vacations.
Check out GENERAL TRAVEL CONDITIONS here:
See Item # 12.