Yeah I interpret it in the medieval sense, where he fights for her, not necessarily like a high school ring exchange. Not that it doesn't have romantic significance. It was a thing in courtly knighthood to be in love with a lady who was unattainable. Wearing her favor wouldn't necessarily mean they had a thing going, but that she was willing to honor him and he's fighting for her.
I think it's the equivalent of a medieval lady giving her knight/champion a garter or handkerchief (or something else) to show her favor. I think it's the red scarf thing that is the favor itself. No idea what the black thing is.
What I like about it is that it shows him moving from sticking around because he wants to "turn and face the tiger" (nice image from Seheron there), to being motivated to stay for Hawke as well.