Usually these kinds of injuries happen during the summer season when new feathers (which contain a lot of blood in its stem) are subjected to trauma like being hit by a stick or being held forcefully. In this case you should secure the falcon and reduce its movement to find the injured feather, you can pull it forcefully by hand or use a forceps to pull it out, in case you are not able to pull the feather, put haemostatic powder to help stop the bleeding and bring the bird to a veterinary clinic or hospital.