Is it permissible to give bank interest money to a poor sister for her daughter's dowry, and what should be done if the money has already been paid?

There is no objection to giving some of the money earned from usury to your poor sister, if your intention is to repent and dispose of the money by spending it on charitable causes. However, depositing money in usurious banks for the purpose of spending the interest on charitable causes is not permissible.