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Hanelion took the money and the ring [and possibly something else; I'll check with Revan, but it's unlikely], leaving the violin and other belongings to burn in the house.
"Hooray, the deed is done. You're probably thinking I'm a terrible monster? Not at all. I'm a noble knight. A noble knight with very sensitive hearing, who can't stand it when someone plays the violin badly. It's just a pity that the culprit who disturbed my hearing is still alive, and in general, there's one extra witness... Oh well."
Hanelion moves far enough away from the house to have an alibi, but still tries to catch a few souls if possible (preferably without a direct view of the house). Then, the dirty, poor old man goes to a place where he can "preen" and transform, ceasing to look dirty and poor. He needs to wash and dispose of his dirty clothes, which were still hanging on him over his robe and made him sweat. It's probably more convenient to do this in the tavern in Tristram, so as not to attract attention to himself.