From Responses, you can easily change the status of a participant, simply click on the current status inside the participant's status box (for example, click on the word "Paid" or "Confirmed" as shown below). You can then change or update anyone's status from here.
The newer Responses makes this much easier - head to the left status column and click to open up the status dropdown, then select the desired status:
It's also fast on the soon-to-be deprecated version of Responses:
You can delete participants if you check the checkboxes next to any/multiple responses, including Select first 100, and then click "delete" from the grey bar that appears at the top of the page.