Do you know if the screen is made of metal or plastic ? Much window screen is made of nylon, which is perfectly safe. I'd wash it well, just to make sure it's clean.
Metal window screen is most often made of aluminum. Bare aluminum in fresh water precipitates minerals out of the water constantly. You'll get big white bumps all over the aluminum, and it will look terrible.
Not toxic, as such, but unsightly and over time it might pull too much calcium out of the water. It's not too hard to get it off, but takes some fairly hard scrubbing to remove it all.