Thanks for the replies - I think for now putting some cloth between the light and reader will have to do for. Some soft flannel or similar would hopefully do the trick, that plastic is pretty soft.
IMHO if the scratches get really bad - to the point I want to spend £30 on another light - it'd be worth investigating plastic polish, like what's used for car detailing. That light ain't cheap!
Luckily I got mine as a gift, otherwise I'd be a bit annoyed.