[mr_toad]

One would hope they’re still in Earth’s orbit - if they’ve achieved escape velocity they’re not coming back.

[exegete]

So if we’re being technical I think they did achieve escape velocity? But the moon’s gravity and some timed burns will slingshot them back.

[gwd]

But one could imagine, as a failsafe, arranging things so that Integrity was in fact still in orbit around the Earth, as a sort of "backup" in the event that they somehow missed the moon's slingshot effect.