Well unless the mirror is 20km across, they won't notice because the whole idea is insane.
This is like the Romans thinking they are going to build aircraft, we are no way we are near the level of technology required to do this. This is like stage 2 civilization level stuff.
Very temporary. If it's going to be very has to be close to the Earth or no one will see it. But if it's close to the Earth it moves so fast there's no point, orbital speed for that altitude is something like 7.8 km per second.
The only way to make this work is to have a truly vast mirror and have it out at geostationary orbit, then angle the mirror as needed to turn on or off the sun but then you're going to be covering a significant area of the planet.
To demonstrate how utterly insane this idea is, this is the sort of thing a civilization would do if it decided it wanted to terraform Mars. Doing this wouldn't be the efforts of a single corporation it would have to be a global effort, we don't currently have the capability of putting something that massive in orbit, we don't have a way to reliably control the mirror, we can't even manufacture a mirrored surface that large, and there have been zero studies on the environmental effects of doing this. It would honestly probably be easier to build a space elevator.
Oh and even if we did do all of this, despite it being impossible, it would only work for a couple of years and then the mirror would get pushed out of orbit by light pressure. The only way to counter that is extremely complicated mirror geometries, and even more mirrors, making the total surface area in the hundreds or even thousands of kilometer range.