Appreciate the informative replies and citations. So, I'm a bit of a n00b in such matters so will politely ask how this situation (how to get ill-gotten artifacts of great anthropological value back into the public domain) typically gets resolved.
The idea cited in a reply that such purchases are funding ISIS (chilling to say the least) kind of implies that ISIS (or a stooge acting on their behalf) is the seller so a trace on the transaction should lead investigators to their door where the items can be confiscated and returned to the museum or public collection from which they were plundered.
I'm probably being too naive about how all this works. But I certainly understand the article much better now thanks to the informative replies.