Thank you for taking care of the cat! I'm a softy too in fact my last 4 cats have all been strays. My Maine Coone was left by the previous tenants in the apartment above me, nice. She unfortunately suffered from anti-freeze poisioning from them leaving her out and I had a lot of Vet bills over the years I had her. How can people sleep at night after they have done these things.
One Idea is if they have just moved they are probably still having their mail forwarded so you could write them at their former address and they would get the letter and ask them what they plan on doing -isn't pet abandonment against the law and they know you know their name. Other than getting them in trouble and letting them know what low life scum you think they are it may be too good for them and the cat will be better off somewhere else.