Glass cleaner should clean it off .. if it's really crappy, something like AutoGlym's engine de-greaser spray stuff (purple label) might get the stubborn stuff off. That's waterbased so should be safe.
My best bet is that your current (old?) wipers are just that .. old, and dirty. Clean the screen .. AG glass polish / AG Fast Glass .. then take them off, (careful with the empty arms, never leave them up !!!) and see what happens.
Also highly recommend RainX (or halfrauds own-branded stuff which is cheaper). I hate having wipers on !