Actually Law enforcement didn't catch Ted Kaczynski. He was turned in to the FBI by his brother David.
"One man – David Kaczynski – came to the sickening realization that the Manifesto’s writing style and philosophy closely matched that of his older brother Theodore (Ted) Kaczynski. David and his wife Linda were devastated by the thought that Ted could have spent 18 years terrorizing and killing so many innocent people. But the more they read, the more similarities they discovered."
Wrong, wrong; wrong; wrong; wrong.
That's true, and David Kaczynski is the first to say the FBI's profile was inaccurate. The difference, though, is that Ted Kaczynski didn't want to be caught, and, in fact, might never have been apprehended if it were not for his brother. Ted didn't purposely reveal his identity when corresponding with the FBI, but Malvo and Muhammad did, by repeatedly directing LE's attention to the Alabama shooting -- the one shooting where they were definitely seen and chased by LE.
Perhaps they weren't aware there was an indentifiable fingerprint, but they surely knew the Alabama police would at least ID them as black, and as a pair or possible trio, and that at least one cop got a good look at them.
They wanted credit for what they had done, and I think the money was simply a way to rub LE's nose in it. Why not demand money? They had gotten away with multiple murders, and the cops were still looking for a white van or box truck, obviously driven by someone other than a black man.