De-oxidizing headlight casing

I'm told that the grey, dull look on my 2000's headlights is actually not dirt (which makes sense since it's "inside" the headlight) but "oxidation". I'm also told that the solutions required to clean/remove said oxidation are dirt cheap and therefore doing the work myself would save me a ton vs going to BMW Service.

Has anyone done this? I'm both new to BMWs and pitiful with cars, so I guess I also need to know if this is a wise endeavor or if I'm going to effect wiring in taking these things out that will cost me more headaches/money than just having BMW clean these lamps.