Kitana plays this matchup similar to how she does with Sub Zero. A careful mix of aggression and defense is necessary to ensure success. Above all else, she must keep Reptile from going invisible. That is the only real time that Reptile poses a threat, offensively. The usual mix of offense, buffering fan lifts, tosses, and IAFs will be enough to get the job done; assuming Reptile is visible. When invisible, Kitana needs to find a safe way to unveil him. Use your ears to listen for a jump-in or slide and counter accordingly. If there is no sound after a couple seconds, toss a fan since Reptile is likely walking forward.
Reptile can fight visibly or not, but of course stands a much better chance from the shadows. Don't be afraid to toss acid out to disrupt Kitana and keep her out of your face. As with most characters, don't jump in against her unless it's a crossover or you enjoy losing. If you go invisible, toss a forceball and/or slowly approach on foot, then unleash hell if you get in close.
Kitana has the edge, but Reptile can give her problems if played perfectly. It's either 7-3 or 8-2, Kitana.