C’mon, 2315 time travel devices were much smaller devices than a hat. Besides, just think of the history of the cell phone. Even the black Razors have been relatively short lived. If it were a communication device and time travel involved, it is probably something different than our cell phones today.
Notice how she fades away when she looks at the camera, as if somebody is fading out the scene into another, to cover up the evidence, so THEY won’t catch it?
But now that we know, why aren’t THEY returning to keep it out of the movie, so we don’t find out about it???? /s <;^)
If you read lips like I do, you’d realize she said, “Beam me up, Scotty”—just before she faded away.