Can the hotel booking API tell me whether my customer can pay at the hotel instead of paying in advance?

Yes, in most cases the hotel booking API tells you whether a room is paid to you at the time of booking or paid by the guest directly at the hotel, and this is shown on each rate rather than on the hotel as a whole. The same property can come back with both kinds of rate in one search, so one room may need payment up front while the room next to it is settled at the front desk on arrival.

This matters for your cash flow and for your customer. When the rate is paid to the hotel, you are only confirming the reservation and the money never passes through your hands, so your commission is usually settled later. When the rate is prepaid, you pay the supplier at the time of booking and collect from your customer yourself, which gives you the money sooner but also leaves you carrying any refund if the booking is cancelled.

Be careful with two things. A pay at hotel rate almost always still needs a valid card to hold the room, and the hotel may charge a deposit or a no show fee against it, so your customer should understand that giving card details is part of the booking. The wording suppliers use for this also differs, and a few smaller suppliers do not mark it clearly at all, so the safest habit is to show your customer exactly what the supplier returned rather than a label of your own.

Check with each of your suppliers which payment types they return and how they name them, then show that wording on your booking page so your customer knows before they confirm.