Hi AaronVia,
Thank you for reaching out to Microsoft Community.
You may disable the "Hey Cortana" option through the Cortana app installed on you IOS device. Open the Cortana app, tap Devices > Devices > Surface Headphones. Tap Surface Headphonesagain to manage the settings. Choose Device control and personalization then turn off the Let Cortana respond to "Hey Cortana" option. You may also check this page for more details to Manage Surface Headphones settings in Cortana.
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Kind Regards,
Marrion Y.