If you or I looked at a dead tree, we wouldn't think of it as the best place to sit. Maybe a branch would break. Too exposed. Full of bugs. That's just us though. To a bird - especially a bird of prey - a dead tree in the perfect place to perch. Great views of their prey. Lookout for foes. That's how it was in this particular tree out in the salt marsh. Mrs. Peregrine must have thought "this looks like a great place to perch", so she landed.
Mr. Peregrine probably thought "hmmm. Mrs. Peregrine got the good perch again" and then decided that it was his turn so he swooped in. She initially put up a fuss.
But then he showed her is talons. Now she's thinking "what's with him?"
"Fine, have the perch. I'm outta here"
Now he's thinking "wow, this really IS a nice perch" To the victor, goes the spoils.
Here are some close ups. I was pretty far away, so these are super cropped. You can see that Mrs. Peregrine has bands on both ankles.
Here you can see that Mr. Peregrine is not banded.