The “that” that Gregor is referring to here is waking up late like the other traveling salesmen

The “that” that Gregor is referring to here is waking up late like the other traveling salesmen. Ironically, that’s just what he’s doing here, although we don’t find out he’s late until the next paragraph. Of course, he has a very good reason to be late – he’s a vermin. But the transformation has the unintended consequence of fulfilling Gregor’s wish to be rid of his job.
Ironically, one of Gregor’s main complaints about being a traveling salesman is that he can never establish a lasting relationship with anyone because he’s always moving around. Stuck at home over the course of the story, he’s still unable to make a connection with anyone.