Can the hotel booking API tell me the last date my customer can cancel without being charged?

Yes, in most cases the hotel booking API returns a cancellation deadline alongside each room rate, so you can see the last date and time a booking can be cancelled free of charge before your customer pays anything.

That information comes from the hotel or the supplier rather than from us, so how much detail you get varies. Some rates come back with a clear free cancellation date and time. Some come back with a penalty that changes as the stay gets closer, such as one night charged after a certain date. Some rates are non refundable from the moment they are confirmed, and the response will say so. The deadline is usually given in the hotel's local time, which matters when your customer is booking from another country, because a deadline that looks like the end of the day may already have passed where the hotel is.

It is worth putting that deadline in front of your staff and your customers instead of leaving it buried in the response. Most portals show it on the room result, again on the review page before payment, and once more on the confirmation email, so nobody has to ring the hotel to ask. If your software stores the deadline with the booking record, you can also have it warn your staff shortly before the free cancellation window closes.

Ask your supplier which cancellation details their hotel content includes, and have your developer display the deadline in the hotel's local time next to every rate, so your team always knows where they stand.