Why not try tying some brightly colored yarn to the inside of the screen. You could use regular thread to tie the yarn to the screen, and I doubt this would void a warranty.
IMHO painting a design would not work, you are looking from a dark area generally into the light area (outside), so you would actually not be able to see the design. The yarn should be visible under virtually all lighting conditions.
Hope this helps.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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