There's nothing preventing you from throwing it into the sprint. But then you gotta exchange it for something else you promised the customer at the start of yo

There's nothing preventing you from throwing it into the sprint. But then you gotta exchange it for something else you promised the customer at the start of your sprint. And agile doesn't just mean Scrum and sprints. If your primary way of working is what you described and you are able to get this feedback within hours then Kanban (another agile way of doing things) might suit you better.