The QIE Web Service is a SOAP Web Service. It is best used for QIE to QIE Web Service calls.
To setup a REST Web Service with QIE, you would use an HTTP Listener and then configure it to send the Response from the Mapping or Destination Node.
For your specific case, you can use either type of web service, but the HTTP Listener REST Web Service would probably be the simplest to implement on the client side and provide the greatest flexibility on the QIE side for configuring the interface. Therefore, I would recommend using the HTTP Listener REST Web Service.