The stolen artifact has been returned to Iraqi officials in Baghdad.
Trump Jr. will be paid $100,000 and will answer pre-approved questions at the University of North Texas' A&T Stadium.
The 33-year-old businessman said the president had to tune out negative coverage from the mainstream media.
Mounting tensions between Qatar and its neighbors spilled over in June, when Saudi Arabia, Egypt, the United Arab Emirates and Bahrain all cut diplomatic ties with Qatar.
A report from the Department of Homeland Security outlined how anarchist groups and extreme-right supporters were preparing for an unprecedented confrontation.
Tehran fell out with Hamas when the Palestinian Islamist movement turned its back on Syrian leader Bashar al-Assad in 2012.
They claim that all Arabs without IDs have to be detained until police arrive.
Qatar has accused Saudi Arabia of deliberately making it difficult for its pilgrims to obtain permits to go to Mecca.
The two shipments of chemical weapons from North Korea and bound for Syria were intercepted in the last six months.
Seven of the Boeing 777s will fly Qatari pilgrims from Doha to Jeddah to attend the annual Hajj pilgrimage.
Figures across the political spectrum have criticized the president's remarks.