Giving a bunny complete freedom as soon as he gets to a new place definitely causes the bunny to run and mark EVERYTHING
Tell her she should really keep him in a pen when he’s not supervised, and give him some supervised free time out of the pen. That way, when he starts his territorial marking she can pop him right back into the pen. Just like dogs or cats, a bunny won’t be perfect in a new place without a bit of training!
Also – I have bedroom bunnies, and if she doesn’t let him on the bed for awhile, it won’t change how much he likes to be up there. Mine weren’t allowed on my bed for a loooong time, until they behaved in my bedroom. Once they behaved in my bedroom I made a set of stairs up to my bed. NOW, they sleep on my bed all the time – with no territorial marking (OK, there was ONE pee incident, but I really think it was laziness and not territorial!)
I’d really emphatically recommend she keep him in a pen for awhile, or else he’s just going to keep marking and driving her nuts. She might feel like its mean at first, but it would be much sadder for him if she got so fed up with it that she decided not to keep him. I forewarn every one of my adopters that the bunny WILL do some kind of territorial markings the first few days, and to protect their house (and their patience) they really need to keep the bunny in the pen, and train the bunny in the new environment.