Well a key part of her personality is that she is proud, and unforgiving. If someone besmirches her name, she may challenge them to a duel, as per Demacian tradition. In these duels she offers her opponent a chance to surrender humbly, and if they refuse she kills them. She has never lost a duel.
It's likely that these duels are only between Demacian nobility, so would not occur if Fiora was insulted by a peasant. I don't know what would happen then. She might just duel them anyway, being who she is.
After the scandal that killed her father, Fiora's only motivation is restoring the honour of her house. If a street hag, as you say, is threatening her reputation, then she will not let it slide.
Pride is Fiora's vice, not jelousy. She won't care if someone makes some randy remarks about Jax, because that is no concern of hers. Lorewise, Fiora has made every effort to avoid entering a relationship. She doesn't care about feeling desirable, or attractive. Such trivialities are beneath her.