Thank you for taking the time to post and welcome to the Bose Community.
I can imagine that is quite annoying! However, I'd be happy to assist you to amend this.
When you swipe on your iPad to bring up the Control center, you should see the option to screen record (as I'm sure you're familiar with). If you press and hold on the screen record button, you should be presented with some options. You may find the option there to turn off your microphone when the iPad is screen recording.
Give that a try and let me know if that solves the issue you were having!
Sam F - Community Support