Sure Apple can fix it, but they don't do " work", if you know what I mean. They will simply replace components. The lid can get a bit pricey, since I've not seen the metal as a separate part from the display.
For some, it is more than cosmetic. My 11.6" had a slight marring of the same edge. As a result, I could not fit a hardshell case until it was "remedied". The case has to be essentially perfect dimensionally in order to snap a fitted hard case onto it.
I would first check with a Genius Bar appointment the cost to repair the unit. Then compare that to the same spare part from the likes of ifixit.com, using a Apple Service provider to do the actual install.
Apple can do the repair, but you'll have to contact Apple tech support, go to an Apple Store, or contact an Apple authorized service center for pricing. You can be confident that it won't be cheap since, if I understand your description correctly, the screen would have to be replaced (with an MBA they can't replace just the frame; it's all bound together).