'At the end of the Second World War the crown jewels were recovered in Mattsee, Austria, on 4 May 1945 by the U.S. 86th Infantry Division. The crown jewels were transported to Western Europe and eventually given to the United States Army by the Hungarian Crown Guard for safekeeping from the Soviet Union. For much of the Cold War the crown was held at the United States Bullion Depository (Fort Knox, Kentucky) alongside the bulk of America's gold reserves and other priceless historical items. After undergoing extensive historical research to verify the crown as genuine, it was returned to the people of Hungary by order of U.S. President Jimmy Carter on 6 January 1978. Most current academic knowledge about Hungarian royal garments originates from this modern research. Following substantial U.S. political debate, the agreement to return the jewels contained many conditions to ensure the people of Hungary, rather than its Communist government, took possession of the jewels.'
So, the citation for that section of the Wikipedia article is a dead link, and should probably be listed as [citation needed], but that's a discussion best left to the Wikipedia talk page for the article.
However, this interview with members of the US diplomatic corps who were involved in the exchange and the events leading up to it should provide some insight. It seems negotiations for the return of the crown overlapped heavily with negotitations for Hungary to obtain Most Favored Nation (MFN) status from the US. By leveraging the Hungarian government's desire for these two items, the US was primarily able to extract promises that Hungary would allow emigration for those wishing to leave Hungary. This was a pretty big deal for a Soviet bloc country at the time. The US also didn't want János Kádár, Hungary's head of state, to attend the return ceremony.
a nice article i found in the theme. its in hungarian, has the title: The homecoming of the Holy Crown, and its the reminiscence of Nagy János, former Deputy Minister of Foreign Affairs, who represented Hungary as the Crown arrived on the 5th of january, 1978.
~translation from the article:
the temporary hungarian government asked the return of the crown in 1945, but the american government ignored the request. in 1946 the american government offered to return the crown, but the hungarian government dissuaded them from it. after 1956 the relations between the two governments were not very friendly, what only fixed in the mid '70s, when the two governments decided they both can profit from the return of the Holy Crown.
in 1976 preisdent Ford promised to give back the crown. and preisdent Carter decided to give back the crown in october 1977. the american government asked discretion, but the case leaked somehow, and only a few (but loud) people demonstrated against it.
about the conditions: the american government gives the Crown to the people of Hungary, not the hungarian government. the Crown must be displayed in public. the Archbishop of Esztergom must host the Crown at the airport, and the leaders of the major hungarian churches got an invitation too. the ambassador politely asked the hosts, dont let the current ~President (Kádár János) receive the crown, even better when he will stay away from the hosting. in theory it was a blunt request, but it did not caused much trouble since the President of the Parliament was appointed as the main host. Kádár decided he has other important things to do on that day.
also the hungarian government had to promise they wont send the crown to Moscow when they receive it. the hungarian government could only promise that the crown wont leave Hungary again. another condition, that Hungary would not accuse the US holding back the crown, nor will it sue for compensation. finally they both agreed that neither of them will ask for compensation (for storing, repairing vs. holding back).
final condition was that until the official ceremony the Crown must stay under american custody. what could have caused trouble, so they agreed on that after inspecting the Crown, an american official will keep the keys to its chest, and a hungarian official will stay with him till the ceremony.
edit: typo i found