I just got a scratch on the lens of my action cam. It can be seen as a slightly blurry spot in the center of the image, when the light falls in the wrong way.
Does anybody have experience fixing this?
I have seen posts about rubbing the lens with alcohol, a pencil eraser and other stuff, but it mostly sounds like you are trying to move some lens material into the scratch. But it sounds like it may also impact the good parts of the lens, when you move material around.
As you didn’t write which model of action cam you have I suppose a Garmin Virb Elite, which is the most popular and the lens is very exposed - for this the lens can be ordered as a spare part, including required tool.
It is a Sony HDR-AS100V. I tried to search for a replacement lens, but only found some priced at about half the price of a new camera. Put import taxes on top of that and I could get a Garmin Virb Elite for the same price.
But replacement parts is not my main subject, so people who know where to look might know where to get it cheaper 
As they offer the spare lens for 20 Euro I already assumed the exposed position of the lens without included protection is designed like this by purpose.
Anyway, I know just because I had the same problem, but it was a not scratch in the lens, the other thing whatever it was left its trace, but on first sight it looked like a scratch. I was able to remove it lens cleaner for my glasses and microfibercotton.
I’d not try to polish away a scratch, as this will detroy the anti-reflex-coating for sure.
My next action cam with a GPS will definitely be a Garmin Virb Elite. Right now I have 2 Xiaomi Yi in the mail. But this Sony is still good enough to be a loaner, so I can get my friends to do Mapillary and not be angry if they break it