Byleth has plenty of scars; she grew up on the battlefield after all. She isn’t ashamed of them, even during intimate encounters. Even less so if such encounters are with one of her former students, after all, she knows they won’t be so shallow as to ridicule battle scars.
But seeing them on her former students brings pangs of guilt. Whether their scars are from during or after their time at the Officers’ Academy, Byleth feels responsible for not having prepared them enough for what left those marks. She wonders if they were afraid in those moments, if they were fighting a losing battle.
I imagine any one of her students would comfort her though, and remind her that it was because of her guidance and expertise that they survived the encounters with harmless blemishes.