'She hears me strike the board and say' in the first line lets the reader know the speaker has some built up frustration with the individual mentioned. The father is putting his foot down about the subject. He is just fed up with his daughter's actions and is laying down the law.
'That she is under ban', is the resolve the father has with his daughter until her relationship with the man changes to the father's liking or ceases altogether. This is the father's way of shielding himself from his daughter's actions. He cannot have her close to his heart or she will hurt him more. This does not mean he does not love her, it means he is protecting himself from further pain about the subject.
The daughter has had wonderful friends in the past. The father thinks that of 'all the good men and women', she could do better for herself. 'Being mentioned with a man that has the worst of all bad names', is what the father has the problem with; the mere thought of her