How did they get it back from Disney?
Yoink.
That was going to be my question too.
So, what changed? Usually such a change has to do with some certain people leaving and other particular people becoming decision makers.
I haven't been able to find details, but it looks like a new distributor final was able to buy the rights
https://wegotthiscovered.com/movies/a-conspiracy-heavy-disney-reject-has-already-brought-in-10m-ahead-of-its-july-4-opening/
https://www.historyvshollywood.com/reelfaces/sound-of-freedom/
Various articles seem to indicate that Disney felt the movie was too "alt-right" as the story and movie involved people like Glenn Beck. I am sure for a woke company like Disney, the actor Jim Caviezel is also persona-non-grata.