Washington Bible Museum After-the-Fact Propriety?

"How an American museum is reviving trade in antiquities, and why, in just the past six years, have the evangelical owners of Hobby Lobby amassed one of the world’s largest private collections" (Joel Baden and Candida Moss, 'Can Hobby Lobby buy the Bible?' Financial Review Mar 18 2016):

It isn't that the Greens are looking to make illicit or unauthentic acquisitions. "That's a headache we don't want," Steve Green told us before news of the investigation broke last year. But unprovenanced artifacts beget unprovenanced artifacts. Once it is known that buyers are willing to purchase items with dubious or nonexistent provenance, the market for those items expands, which in turn encourages the kind of looting that we're witnessing today in the Middle East. The connection between a scrap of papyrus and on-the-ground violence may be difficult to see. But it exists. And that is where the real danger of hiding provenance lies. The pace of their acquisition alone suggests that the Greens may not have taken every possible step to investigate the provenance of what they have bought, a risk that they acknowledge. "We do what we can," Steve Green told us, responding to the question of whether his family has knowingly acquired problematic artifacts. "But there is the risk that after the fact, you find out it wasn't appropriate for us to buy it."

But then the true measure of propriety is what then happens to those carelessly-acquired items of illicit cultural property, isn't it? What is the "Bible Museum"s policy on these past "inappropriate acquisitions"? Should they be in the collection? Should they be on display? Obviously not.