Sure, just transmit stronger white noise on 433.92 MHz. I haven't looked up who owns that frequency and whether there are restrictions.

Or get a GPS blocker. Which I think are illegal to operate.

AFAIK 433MHz can be used for any short-range application, similar to 27/49MHz for R/C cars. There are plenty off-the-shelf 433MHz transceivers for hobbyists, and I think car remote-unlockers use that band as well. And this doesn't appear to have a particularly powerful transmitter, so you'd have to bring the transmitter relatively close to the receiver (like <100ft, usually) in order to download...whatever.

If they're able to put this thing on your car in the first place, I guess it's not infeasible for them to drive by to download updates.

Sparkfun sells 434 MHz transmitters for $3.95 [1]; just hook it up to a coin cell or four, and you should be good to go.

[1] http://www.sparkfun.com/products/8946

I wonder what would happen if you took it off and attached it to a random other car. Then the FBI would be tracking someone else illegally, in theory.

I would bet intent is part of the law.

Why would tampering with such a device be illegal? Or blocking their signal? It's your car and until proven otherwise, you have no reason to bear with other people or the government installing such surveillance equipment.

If you're a convict then you might be released earlier but with some electronic surveillance, but even that is with your own consent.