This is a great thought - nailing the ADL for trying to coopt Gunner.
I'm not an attorney, but.......
I'm not so sure you're out of luck, or rather your brother. I think there's a concept of 'appropriation of image', which is why when the news team comes to school to interview some teacher in the classroom, they try to get the parents to sign a permission/authorization. By image, I mean Gunner's look , not just the photo itself, though that may be another angle.
Then there's possible 'privacy' invasion, but it might be tough to argue the privacy of an animal that routinely relieves himself in public......
Since your brother's dog has become sort of a web star on other sites, probably with express permission (even if verbal) he may need to get some intellectual property attorney to tell him how to protect and control the use of Gunner's image. If he can't find one, maybe an actor's booking agency can help him look.
There may also be self-help (like 'Nolo Press') books on the matter with good advice and even form letters (though I would retype & avoid any kind of appearance of a form letter), though you often wind up wondering about whether the attorney would be better.
But your brother is the one who should control the use of his dog's image & likeness.
To keep the ADL from claiming copyright on Gunner's image, your brother should challenge them as soon as he's gotten some advice on how to do that.
It may also help to formalize any existing permitted uses and get some compensation (get advice on how to structure this)so that the ADL can not claim that it is being given away.
Since a lot of wacko liberals are probably visiting the site and admiring the dog, maybe a per-visit rate is in order.
I wouldn't be surprised if they just take it down on demand.
[red][size=4] P.R.K.