Well, my old Oxford says that the term dates back to 1584 and was a variation on Jew's Trump, which term dates back to 1545. In Scotland and the north of England it was just called Trump, which also agreed with the French term trompe. It also says that the "Jew's" part of the term was always there but only in English. There is nothing about why or how the Jew's term got appended.

Oh, well. Twang away and to heck with the name of it!