Bizarre client request experience

Received a change request which makes absolutely no sense for what we are building right now.

Reason? Apparently, they want the mobile app to sync live user data but strictly without connecting to the internet for security reasons. Had they specified this in the initial scoping itself, I would have politely explained how technology works. But no, they had to tell this on Monday right before delivery.

Our team is already overworked and when I mentioned my disbelief that I was expecting standard cloud integrations let alone offline magic to finish this, they ridiculously asked me to just code a workaround using Bluetooth. They'll try to pitch it to their leadership in a way that sounds like a proprietary network. So what now, am I supposed to be inventing new laws of physics to meet their requirements? Am I not supposed to be building actual software?