WASHINGTON — The line of people snaked around the blue tablecloth, as government officials and archaeology scholars paused to admire the ancient clay tablets and seals lined in rows.

Here, in the backyard of the Iraqi ambassador’s home on Wednesday, was closure for these artifacts: a ceremonial transfer back to Iraq, where they had been looted from archaeological sites. Their coming return there will complete a long, circuitous voyage through Israel and the United Arab Emirates to Hobby Lobby, the arts and crafts chain, and eventually into the hands of the United States government.

The samples carefully lined on the table were just a small fraction of the thousands of smuggled artifacts that Immigration and Customs Enforcement formally returned on Wednesday.

“To have them in my residence is to underline that they’re coming home,” said Fareed Yasseen, the Iraqi ambassador to the United States, speaking after he and Thomas D. Homan, the acting director of ICE, signed the ceremonial transfer. “We really have a sense of kinship to these artifacts.”