This has been covered in threads before. It is almost impossible to remove any marks, stains, or fingerprints from a reflector. Anything that touches the reflector wil most likely scratch it or stain it. Never touch a reflector even with gloves on.
If you assume that you will damage the reflector by doing anything more to it, that will let you judge whether you want to leave it alone or just go ahead and order a new one. If you do order a new one, you then have a backup in case you want to go ahead and try to clean it.
If it were mine and I wanted to try to clean it, I would first start with a camera lens cleaning solution. If that does not work, I might go to a glycerine based soap in a very mild solution. Finally, I'd try a mild soap in a mild solution. But as for washing a reflector, almost anything is going to leave a residue at least and at worst will further stain or remove the silvering. Plain water (even distilled water) will waterspot them.
I have heard of people trying to use a lab-quality pure alcohol as a rinse. I have no idea as to how well this would work or where you could get some.
For dust, you might want to get a lens cleaning "puffer" brush from a camera shop. These are bulb and brush gizmos that are used for cleaning camera lenses. Never use compressed or canned air on a reflector. Start with a puff of air and then work up to an extremely light touch with the brush. BTW, get the softest brush you can find -- do not try to save a few pennies here. Light dust and/or a hair or two comes off, anything more does not.
Again, I always assume that any reflector I try to do something with is always going to be worse when I finish. The best I have been able to achieve is making it a different but no worse problem.
Plain and simple, I find it is easier to replace these than to try to clean them. It just ends up being more costly in time and money.