US WWII or Korean shoulder patch with Greek and Turkish motif

[JKK]

If it's Korean War, I hope I did not commit a forum foul by posting. This odd patch, which seems rare, has a Greek style cross and the Turkish crescent and star, but came from a US Army vet. It's possible it is some form of liaison unit from the Korean War, since Hellenic and Turkish forces both served there, though I would think it a very odd thing for us to combine the two on the same patch (and I think Turks and Greeks might find it even odder).

I recognize the KMAG patch and the 90th ID patch. Not sure about the little brass-colored pin.

[HPL2008]

The patch in question is for the Headquarters, Allied Land Forces Southeastern Europe, established 8 September 1952 at Izmir in Turkey. The patch was worn from 29 October 1952 to October 1989.

(Source: U.S. Army Patches, Flashes and Ovals. An Illustrated Encyclopedia of Cloth Unit Insignia by Barry Jason Stein.)