-던가요 asks the listener to search their memory and report what they saw or experienced: 그런데 저희가 혹시 만난 적이 있던가요? 'have we met before?' It is the polite question form, common in interviews and in gentle probing about someone's past. One line here uses it differently — 차라리 돈으로 주시던가요 is a grumbled 'you should have just given money instead', a sarcastic suggestion rather than a question.