Trademark rights are not inferred due to registration but mere use in a commercial form. If they have used either term in commerce, they do have at least some trademark rights in the name. They likely have used the name in many various commercial activities and as such, may have a claim to a wide range of rights.
That doesn't mean they have a right to claim the domain name though.
the big issue I see that is a negative for you is not the use itself but relating it to your specific use; gambling. They may be able to develop that into an defamation claim since you connecting them does infer they are involved with your gambling situation.
With that in mind I gave the site a theme related to an online poker fraternity.not sure what that means exactly but from my perspective, it makes it worse. It really suggests a connection between the PBS group and gambling and YOU are the one that made it appear that way.
Since it really isn't that valuable to you, my suggestion would be to relinquish the domain but I'm not all that altruistic in nature. Since they let the domain registration lapse which is what allowed this scenario, I would offer to sell it to them, at least to recoup whatever costs you have regarding the domain.

