It is really jarring to see differences in perception of things. I can't imagine a world where some reddening from a slap would warrant a bandage or even gauze. That isn't to mention to use of a cowl. I suppose it is played up to give some more reason for the apology, without causing a more violent starting event, but it just comes off halfassed, because of that.
I would laugh though, if I saw someone using a bag of frozen peas or a frozen steak, as a stand-in for an ice pack though in one of these comics.