These pads have worked well for me in situations where I am wanting to provide cushioning assuming there is a place to stick them on the back of your projection screen:
https://www.amazon.com/gp/product/B00DHNIKHC/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
https://www.amazon.com/gp/product/B003IMJ3S2/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
https://www.amazon.com/gp/product/B002OTNGPQ/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
You can also use felt pads.
Much depends on the magnitude of the forces involved.
As far as rattles at the screws, the weight of the screen probably prevents vertical vibrations.
If you screws are solidly in studs, I would look to wedge something between the frame and the wall. I don't know how sturdy your frame is, but Ideally the wedges would be close to where the screws are so the frame doesn't bend, but far enough away to allow the frame to flex just a touch to maintain forces between the frame and the screw. If your frame is rigid, you can go farther from the screws. If it is frail and subject to getting bent, stay close to the screws.
I hope that makes some sense to you!