the data is saved only in session e.g. in global variables or parameters
You could not save it locally on the end device because so far I know is this not allowed / no such permission.
But you can save the data back to the server. For example you can use a Thingworx service to save the data into a thingworx thing in a property or you can generate some json in session and save it into Thingworx repository. So if we want to save some data to a file we need to use a thingworx FileRepository thing - in this case the service SaveText (for text files) SaveJSON, SaveImage respectively for JSON or IMage file and SaveBinary for binary - but it could be used in generally for any file format.
I think it is in generally possible to save data using some resp API call to any server which are allowed regarding the CORS setting for access