After Levis squad other than you died from the female titan, Levi took extra care with the bodies. He ripped Petras badge off to remember her by however he saw a scout more distraught over his friend. Levi was tearing up inside however he gave the badge to the scout. It helped the scout however Levi was holding on by a thread. You notice it took some resistance to let the badge go. He was constantly wiping his eyes and dabbing his nose with a handkerchief. He's losing it. Slowly. But he's definitely losing it.