The "heist", which presumably gets covered in part 2, is that a lot of these items were originally looted from Iraq after the US invasion in 2003. US Customs ended up seizing a lot of them, and about 15,000 items ended up having to be returned.
In doing so, I doubt that they broke any export regulations.
And entrance to the British Museum is free, for everyone.
[0] TFA links to https://www.slideshare.net/slideshow/dead-men-tell-tales/148...