^^^That is nutty.
I can understand not saying where a SWO is because people can literally walk up and grab it, but a Gyrfalcon? Good luck getting anywhere close to it AND there are so many Peregrines around that if there was a problem with what you are talking about, Peregrines would dissapear. Peregrines are not dissapearing and all of them are watched very closely, and have been for well over 10yrs in this city, so we would know.
I highly doubt this is a Gyrfalcon. They dont hang out in trees in backyards. They stick to cliffs, bridges and tall buildings. If you said that you lived beside a bridge and there was one hanging around on it, or in a condo and one was on your balcony a lot, I would be more inclined to think that this very rare visitor was indeed a GF.
Do you live in Leslieville? If you cant get pics, I live close by and would be able to give your Coopers Hawk, Merlin, or Redtail, or maybe even Goshawk an ID. It is almost certainly one of those.
Is it smaller than a crow, same size or bigger?