When I saw they wanted a 'round the back double "knee" grab I thought that was great - so I tackled the poor guy!
羽交い はがい hagai is wings or pinion. 羽 is feather, wing, or sometimes blade. 交 is a lot of things I guess. It is interchange, mix, blend, etc. In this case hagaijime is pinioning nage's arms from behind (ushiro). If uke has nage in this position it looks like a bird with it's wings held back.
I guess you don't have to grab near the elbows but that is where I have seen it the most and it seems easiest. So far as I know.