Do this at your own risk. I have no idea what the long term effects are but I have been doing it for over a year and everything seems fine.

There are a few different ways of tackling cloudy carbon fiber but most of them require a lot of work and buying stuff. If you are OK with a fix that lasts just a few months then you may already have everything that you need:

Tube of clear RTV silicone (yes, the adhesive)
strong paper towels (the blue shop ones are best)

Apply a very small amount of silicone to the problem area and then immediately wipe it off with the paper towel. Scrub as hard as you want because you eventually want to remove it all. The extremely thin film that remains will magically make the cloudiness disappear.

Once the paper towel gets loaded with silicone you can cover a large area rather quickly. Just keep moving and don't let it dry. If you know of a way to safely water down the silicone then that would help a lot.

If you have ever tried heavy wax to fix cloudy carbon fiber then this method seems to last several times longer. The drawback is that it can be a little streaky. Use a couple of clean paper towels to remove everything that you can and then come back the next day and wipe it off again.