A few weeks ago, I said that my Remus has no scars, because there is no canonical foundation for them; i.e. Harry doesn't mention any when describing Lupin's appearance, whereas he mentions the lines several times. Scars are much easier to notice than lines, so, no, Remus hasn't got any.
That's my canon-based reasoning. There is another aspect I'd like to mention, triggered by something
penknife said in a recent post of hers: "They're not book canon, and I think you can argue strongly from canon that Remus doesn't (for instance) have visible facial scars, because that's never mentioned in descriptions of him, and it's something Harry would notice. And yet I can see how I could use them to good effect in fanfic."
While I can definitely see how scars can be used to good effect in fanfic (or fiction in general, for that matter), I prefer to have Remus scar-free because of the increased angst potential. I feel as though being left without scars, after slicing his skin open month after month, year after year, would make the whole experience even worse than if he had scars left. Scars are important to remind one of what they've been through. Being hurt time and again without any visible traces is like having all bad memories erased from one's mind. I have my Remus secretly crave for lasting wounds and scars, because while they heal, he destroys himself anew each and every month. It's an experience of almost Prometheusian dimensions, and oh such good breeding ground for Teh Angst!
*pervs over UnblemishedSkin!Remus*