After you're done printing an image (registration mark, ganged print, etc.) use freezer paper (available at grocery stores) to cover it up. Cut a piece a little larger than the image you want to cover and fasten it to the shirt side of the screen (coated side toward the mesh) with a few pieces of masking tape.
The freezer paper is waterproof so the ink can't soak through it and because of the coating it won't cause your screen to clog the way regular paper will and it won't gum up like tape.
After you're done printing, pull the freezer paper off, run it through your dryer to cure the ink and throw it away.