I didn't get how Julius tarnished his career. Also it was not mentioned how he went out of his way to save Subaru?
Julius challenged Subaru, someone who is clearly below his rank, then during the fight he practically started bullying Subaru, who was obviously greatly inferior to him regarding fighting abilities.
Julius is a knight, meaning he should live by the Knights Code of Chivalry, but his actions mentioned above are clearly violating it.
The duel had a lot of witnesses, so these events ruined the public view about him while leaving a stain on his whole knighthood for a really long time.