The U.S.GAO recently released a report on 15 August 2016 that details the Cultural Property Protection of Iraqi and Syrian Antiquities.
“The Islamic State of Iraq and Syria (ISIS) and other groups have seized upon the conflicts in Iraq and Syria to destroy, loot, and traffic cultural property, including antiquities. According to the United Nations (UN), this destruction and looting has reached unprecedented levels. The UN has also reported that since the civl war in Syria began in 2011, ISIS has used the sale of looted Iraqi and Syrian cultural property to generate income toe strengthen its capabilities to carry out attacks. Under the Convention on Cultural Property Implementation Act, signed into law in 1983, and other laws, the United States has restricted the importation of certain, but not all, Iraqi and Syrian cultural property.”
Here is a link to the GAO webpage, with a downloadable pdf of the full report. We suggest you read it.