How did that get there?

Whether it was the Fallen, The Hive, or meteors that damaged it, some thing moved it into the Moon's low orbit.

Hypothesis, based almost entirely on speculation: The Mars astronaut video is captioned 'present day', implying that the mission to Mars took place while the ISS is the largest orbital hub of activity. Any Mars-going ship with current technology would have to be assembled in orbit if it was delivering a capsule-sized payload and capable of a return journey. Thus, the Mission to Mars 'launched' from the ISS. After the discovery of the Traveller, rather than letting the ISS' orbit decay after its intended lifespan, the space station was instead restored and kept as an in-orbit monument to the mission that discovered the Traveller. After the Collapse, the Hive towed the ISS to low lunar orbit as a trophy. We know they hate humanity. We know they're partial to things like keeping the bones of dead people in huge piles. Nomnomnom trophies. What better trophy of the triumph of the Darkness than the launching point of the mission that found the Traveller? Also, due to low / nonexistent lunar atmosphere, an object could orbit at a very close distance, as we see the ISS doing.

Maybe it felt like it? (Just kidding) maybe the fallen (or possibly hive) took it out in an attempt to make a statement to humanity or something like that.

Took a hit from something and then got caught in the moons orbit is my guess.