Did the Hanseatic League have any policy toward or involvement with Jews?
The cities of Hanseatic League belonged to different countries and a quick search indicates that they did not have a common policy with respect to Jews.
Of those countries, the most tolerant one to Jews was the kingdom of Poland, which later merged with the Grand Duchy of Lithuania, which evolved to Rzeczpospolita Obojga Narodów, which is translated as Polish-Lithuanian Commonwealth, but literally means Republic of the two peoples). These countries in general granted various rights to Jews (the policies varied with time), and had substantial Jewish polulation. In general the Rzeczpospolita was by far the most tolerant state in Europe with respect to religion.
On the other hand Jews were not permitted to live in most of the German and Russian controlled cities See, for example, http://www.jewishvirtuallibrary.org/jsource/judaica/ejud_0002_0013_0_12843.html and http://en.wikipedia.org/wiki/Jewish_community_of_Gda%C5%84sk
I cite from the second reference: