Lets not ask how long before... lets ask how long are you waiting to clean it?
I also have never herd of a screen becoming toxic.
Can you please post a picture of your setup?
Pictures of the screen and/or harvest would be helpful.
Also if it happens everytime, it maybe helpful for the community if you video'd it.
Setup a phone or camera and video you removing the screen and then the fish behaviour.
Can you test the water? What are your readings?
How old is your tank?