Slightly more expensive, but Aedre could get scuba gear and immerse herself in a sticky substance and wait for it to dry. Eg, she goes in a room with the drone, then seals off the door and triggers the room to fill with amber. Amber dries, she chips her way out, done is stuck.
A costly method is go see an expert drone remover. Of course, you can't tell the guy "Hi, there's a drone following me that will kill me if I talk about it"... but merely sitting in the expert's office and chatting about your day should be enough - if he's an expert he's used to clients doing just that. He'll be like "nice day. Can you lend me 20 biluvian dollars?" Aedre passes over the bills then whisk-whisk no more drone.
A much less involved method (though much more hardcore) is to hop in a ship and travel a few light-hours or light-weeks away. This means whoever's watching has a huge delay in the broadcast. She can take all the time she wants to get rid of it (I doubt they make hyperspace communicators tiny enough to load in the drone based on tech level presented).
A cheap, hardcore method is to hop in a cryosponge for a 50-year journey, then turn around and come back. 100 years round trip - all your enemies are dead. Problem solved.
A more involved method is to try to wear the thing out. Seeing at it can't have infinite power there must be a charging system (solar? Electromagnetic transduction? hydrocarbons? Antimatter?) Just hang out where it's dark, or no rotating core / magnetic field or in a desert etc. Or spray metal-dissolving acid all over the place. Set the room on fire (be careful with that one - hire a professional pyrotechnics engineer)