If you get stuck with a distracting branch like this, let's look at the positive side. Immediately I though of florida and their cool air plants. I guess this kind of establishes a sense of place. Any other distracting branch just would not tell us where you took this. ;-)
I love the nice color, light, and pose. The branch above with that dried leaf provides a frame and environmental setting and is not a real problem. The only think I might remove is the small, vertical, out of focus branch directly above the hawk's head.
Beautiful colors. I actually like the framing upper branch, but agree on the small twig over the birds head. I find the brown leaf on the rear branch a bit distracting, but overall, a very nice image.