Question

Why does De Levis come to Dancy's flat soon after? What appeal does Mabel make to him?

Answer 1

De Levis came because Dancy had come to his rooms when he was out. The day before he had threatened him, De Levis didn't want Dancy to think that he was afraid of him.
Mabel appealed to him to behave like a gentleman with them just as he should want them to behave with him. She told him to withdraw that wicked charge, and write an apology which Dancy could show.