I think they found his finger prints in the house were Jon Benet was killed. The fact that he had never been in any trouble with the law at the time of Jon Bene's murder would mean there were no FBI finger print file on him in 1996. It wasn't until 2001 that he got in trouble with the law. By then they were not likely checking finger prints with the FBI. After 4 or 5 years they would give up finding a match.
This DA ia a sharp cookie.. She would not have Karr brought back to the USA if she did not have compelling evidence of his guilt. We know it is not DNA, and it is not his confession... then that leaves finger prints.