In Predator 2, the government organization who were put in charge of hunting this creature down had that specific place on lock down. They may have certainly picked up the hand for their own research.Furthermore, i'm certain Harrigan didn't just walk away from his encounter with the P2. He even told the agents that they will get their chance in the future. He was supposed to return somewhat in Predators but that was cut.
The hand piece simply solidifies the government organisations cause, it gives them a motive and solid proof that these creatures truly exist. Whereas in the first film we only get a testimony from Dutch and that woman. And the evidence of a nuclear explosion witnessed by the helicopter.
Other than that there is no solid proof that it truly exists, however, it is almost certain that they capitalized on Dutch's testimony and experience and did further research into the matter. After all, it killed all of his men and he was sent to encounter the creature...
In P2, the agents utilized Dutch's information.
The Bomb gauntlet was shattered to pieces last time I checked.
The hand would only mean that they have solid evidence that these creatures exist and that all their funding was not in vein.
The government organisation are interested in the weaponry that the Predators have. We see at the end of AVPR their fascination with wolf's plasma pistol.