Klaue's crimes against Wakanda were theft and smuggling... Outside Wakanda he was involved in murder, arms dealing and international terrorism.
Regardless, I don't think it even matters if there is any existing extradition agreement or not. T'Challa's entire Kingship is predicated on the concept of opening Wakanda to the world in order to make it better. That absolutely 100% requires Wakanda to gain the trust of the world, and you just don't do that by rewarding terrorists or murderers with total freedom from prosecution. If T'Challa did set Killmonger free within Wakanda, it would torpedo every hope and dream he could've ever had of actually influencing and improving the world.