it seems having the kind of upbringing their family have, Dion seems to find solace with Ana since she's the only one who openly showed him some kind of emotion, though it wasn't love but still an emotion, regardless. He's quite determined to have some kind of impact on Ana that will never leave her, so I guess a "scar" in a way is a good metaphor. He wants to leave an impression on Ana even if it's a bad one.