Bald Eagle FTW!
Murrey is smart enough to gather evidence about what the Army is really doing in Hawkins - which violates everything from Posse Comitatus to Federal Law on kidnapping, torture, murder and illegal human experimentation. And he's paranoid enough to leave copies with someone he trusts, probably a lawyer. Or more likely, several lawyers, who have instructions to send the evidence to major newspapers and TV stations should Murrey ever die, vanish or be jailed.
Add to this the fact that, with El, "dead" and the Upside Down destroyed, the entire operation is a wash. Kay might want to punish the heroes, but her superiors will probably be pragmatic enough to cut their losses. As long as they keep their mouths shut about what actually happened, the Party are free to get on with their lives.