Until the pet parent actually books and pays, an enquiry comes without any obligations for either party. To turn an enquiry (status "Contact") into an actual booking, you need to make that booking and payment after a successful Meet & Greet with the pet sitter.
This also means that there is no need to cancel an enquiry. If the you end up not booking, or the pet sitter can't take the booking after all, the message thread of that request will simply expire after a while.
If your dates have changed since you sent the enquiry, you can either start a new request or, if you and the pet sitter are in agreement about all the details, you can book directly on the pet sitter’s listing by selecting the service and period from their price list.