The ICE and CBP and Illicit antiquities in the US

From the US Customs and Border Protection website:

As the largest investigative arm of the Department of Homeland Security, ICE plays a leading role in investigating crimes involving the illicit importation and distribution of cultural property, art and antiquities. ICE’s Cultural Property Art and Antiquities unit and Office of International Affairs work jointly to identify, investigate and eventually return art and cultural items to their countries of origin or rightful owners.

ICE uses investigative authority to seize cultural property, art and antiquities if they were illegally imported into the United States. It also investigates the illegal trafficking of artwork, especially works that have been reported lost or stolen. ICE’s Office of International Affairs, through its 63 attaché offices worldwide, works closely with foreign governments to conduct joint investigations.

CBP is the unified border agency within DHS charged with the management, control and protection of U.S. borders at and between official ports of entry. [...] CBP is charged with keeping terrorists and terrorist weapons out of the country while enforcing hundreds of U.S. laws.

But still huge numbers of fresh antquities seem to be appearing on the US market under their very noses. Have they all got export licences? To what extent has anybody actually checked?