You have a military government which is run by essentially a dictator. He has his own citizens that he doesn't give a crap about and he has the concept that some of them may have illegally gone to the US.
You have the US which claims they have people that are illegal immigrants from that particular country or the border countries but they don't want them. And would you please take them off our hands?
So the military running that country says sure, you going to do us favors in the future? Of course we will. Well then send them to us and we'll be happy to throw them in our jails.
Negotiation over.