Don't see why you're downvoted for posting this. Certainly, satellites designed before the Space Shuttle would have to be very paranoidly designed to include a self-destruct mechanism, but it only takes a couple kilograms of explosives to strongly disincentivize kidnapping it.

If I was a military satellite designer, heaven forbid, I'd definitely include that in a world that included the possibility of stealing satellites. The capability, quietly communicated between the powers, would be enough to ensure that the satellite would never be stolen. And therefore, the billion-dollar kidnapping capability becoming useless.

Even without self-destruct, a satellite not programmed to be captured could simply fire some thrusters if it detects an orbit change, and that would likely make some big dammage inside the capturing shuttle.

As part of just normal station keeping it might do that.

That's typically ion thrusters, isn't it? That's very low mass at very high speed, and would probably take hours to even leave scorch mark. It would feel like a slow breeze.

Of course, military use could do something different, but that's more along the lines of "pack a kilogram of explosives in a pipe bomb".

Hydrazine thrusters more likely. Ion thrusters are novel.

Even without that inclusion you could still communicate it :) Save some money and more payload.

I agree with you that hostile satellite recovery would be fraught with challenges. That said, I expect there are people who 'war game' these scenarios all day and probably have various counters or techniques to prevent damage to the shuttle or its bay.