How does pay by group mark the order as paid if they send payment directly to our gateway or bank account instead of passing it through the order api? what if the order api requires a credit card to be a valid request?

There are several solutions, and which is best depends on how your API works and your sensitivity to processing costs.

No Payment Method or Marked Separately - Your Order API does not require any payment method, so Pay By Group calls your Order API to create the order without issue. You treat the order as valid and receive payment separately. If needed, Pay By Group can make a separate call to tell your system payment has been made for that order.
Pay By Group Payment Method - You allow Pay By Group to pass “Pay By Group” as a valid payment method via your Order API. You treat all orders made using that payment method as fully paid because Pay By Group will have captured payment at the time the Order API is called.
Single-use Credit Card - Pay By Group will generate a single-use credit card for each order and pass it through your Order API. Your system will charge it like a normal order, and Pay By Group will not send payment to you separately, as you already have it. The disadvantage of this option is you incur 2X the processing costs - 1) the cost of Pay By Group’s processing the cards for each group member and 2) the cost of processing the single-use card through your processor.

Pay By Group