Excuse me, but the issue is not whether the company has a legal right to the URL. That's clearly something a lawyer can advise you on. But what you really need to decide is whether your good relations with the company are more important than any benefit you might get from keeping the URL.
On the face of it, since you've already abandoned the URL, it looks like it would be worth your while to accept their offer in order to maintain good relations with them (I'm assuming that they are your supplier and that you are successfully selling their product). But remember, everything is negotiable. Perhaps as part of the deal, you can get them to help publicise your new URL in some way.
At least, that would be my advice off the top of my head. But that's just based on the few details you have given. You can't expect anyone here to give a considered opinion without knowing more of the facts.