Does Olga Kurylenko have a scar on her back?

no

.....actually no and yes -

The movie version: Camille has burn scars on her back from when General Medrano set fire to her house after killing her mother and sister. Camille was trapped in the house for a short time & was subsequently burned. The actual reason is that actress Olga Kurylenko had tattoo laser-removal surgery just before filming commenced, so they worked it into the story for the film.