  From the basic concepts of general relativity, we investigate the rotation of
the polarization angle by a moving gravitational lens. Particularly, we clarify
the existing confusion in the literature by showing and explaining why such
rotation must explicitly depend on the relative motion between the observer and
the lens. We update the prediction of such effect on the double pulsar PSR
J0737-3039 and estimate a rotation angle of $\sim 10^{-7}rad$. Despite its tiny
signal, this is $10$ orders of magnitude larger than the previous prediction by
Ruggiero and Tartaglia, which apparently was misguided by the confusion in the
literature.
