Why is the "la chose" replaced by "le" instead of "la" in the following sentence?

The antecedent of le here is not la chose, but the clause « que vous faites cette chose ». This is given le, masculine singular, only because that functions as the default inflection when gender and number don't apply.

It's definitely tempting to find the nearest noun for a given pronoun. But certain pronouns, especially le and en, tend to associate themselves with implied elements of the discourse:

Est-ce que tu as bien aimé Anne ? Et dire qu'aujourd'hui, tu le regrettes.

Personne n'a écrit un livre sur comment en lire.

It might be helpful to realize that in English, we often give these elements no pronoun at all. We just omit them:

— He's coming back at midnight. Il revient à minuit.
— I know. Je le sais.

Here le refers to « qu'il revient à minuit », but there's no corresponding it for "that he's coming back at midnight".