Unfortunately the white layer will never actually "turn" green again. What happens is that the turtle has to grow & shed his shell. The shell material is kinda like your fingernail.....if you damage your fingernail you just have to wait till it grows out to look normal again. Unfortunately this can take years for a turtle since their metabolism is just so darn slow. The good thing is that his shell does not look gray in the picture.
As long as this turtle is receiving the proper care (good basking light, heated water, variety of food, clean water, calcium), he should be able to recover eventually, but it could take many years. I see from your picture that he has grown since you got him & in between some of the scutes I see dark green areas. The turtles "stretch" when they grow and the way the shell looks inbetween the scutes (as they grow) is a good indicator of how they are doing & if they can ever grow out of a shell problem.
On the other hand, Turtle_nz's turtle looks like he is getting ready to shed his scutes at some point in the future. That is a very normal thing. The layers of shell do not last forever & will eventually get old & peel off. Before they peel the scutes do turn white as in the picture.
Hope that helps! Just be patient & give the turt some TLC.
