Extraordinary rendition is a modern US eupehemism for exporting people to other countries so as to torture them. Even the Google definition - "the extrajudicial transfer of a person from one state to another" is interestingly phrased - "extrajudicial" !!!
In law, rendition is a "surrender" or "handing over" of persons or property, particularly from one jurisdiction to another. For criminal suspects, extradition is the most common type of rendition.
I prefer the idea that rendition is the "performance of a musical composition or a dramatic role" - i.e. these poor folk are taken abroad so as to make them sing!
1 week ago