I don't think the bird is an escapee from a falconer for multiple reasons:
1) It is a juvenile. Juvenile Gyrfalcons are known for vagrancy. They show up much further south than the adults. That said, this is ridiculously fr south for a Gyr.
2) It is a brown bird. Gyrfalcons used for falconry are the white morph birds of the high arctic. For an intellectual exercise, I went on the internet to buy a Gyrflcon. There are not a lot for sale, and they are very expensive. The odds of some dumb guy losing his $50,000 imature brown bird are absurd in totum.
Click here to see photographs and read about that obvious escapee.
The Kestrel constantly harassed the Gyr.
That's like a Dachshund attacking a Pit Bull.