It is likely that these requests are generated by some software that runs on the Browserstack virtual machine or in the Browserstack network tunneling application rather than by TestCafe. Maybe, these requests come from a third-party script on your page, like Google Analytics.
If you can't give me access to your page, could you please provide some information?
How does this problem affect your testing experience (tests don't start/fail silently/there are errors in tests, etc.)?
What is your Browserstack virtual machine configuration (the OS version, browser version, device type)?
What frameworks and third-party scripts are used on your page (Angular, React, Vue, Google Analytics, etc.)?
If you have access to the Browserstack Live Testing, you can also open your page in Live Testing mode with Browserstack Local but without TestCafe, and check if the problem persists.