What is the best practices for retrieving data from cross origin JSONP API with Origin header restriction

What is the best practices for retrieving data from cross origin JSONP API with Origin header restriction?

The website it self use JSONP to fetch some data from its backend. I want to perform the same action in my WebExtension content script. What I have tried:

  • Access JSONP API data using fetch() API and parse the result
    • It failed because Origin HTTP request header is not set. The website refuse to return result in such case.
  • Access JSONP API data using content.fetch()
    • The request is blocked due to CORS policy
  • I’m not sure if it is possible to work it out on background script, but it will lose contextual identities information

So what should I do then?