If your windows are already scratched or looking foggy, can transparency be restored? Maybe.
Damage occurs first on the surface of the vinyl, so if it is not too deep, you may be able to remove the damaged layer with an abrasive. Start with a plastic polish, something like Meguiar's PlastX, and see if you can buff a small corner to clarity. If the answer is yes, you can restore the whole panel the same way.
Vinyl beyond the repair capacity of polish can be compounded — just like dull paint. For this you need a very fine glazing compound — 3M Finesse-It II or equivalent. You will also need an electric polisher or a variable-speed drill fitted with a rotary backing plate, plus a couple of foam polishing pads. Wash and dry the vinyl, then place it on a flat table padded with a bedsheet. Apply a squiggle of compound to the vinyl, then machine polish a small area, keeping the polisher moving and the pressure light. Use a trigger bottle to keep the compound moist. This is a learn-as-you-go process, so get your practice in on your least conspicuous window.
Wash the vinyl thoroughly to remove all compound residue, then do it all again with a clean foam pad, only this time use your plastic polish and do not moisten with water. The polish will leave behind a haze that you will need to buff off with a soft cotton cloth. If your polish does not provide UV protection, finish with an application of 303 Aerospace Protectant.