After using an object do you replace it with rubble?

In the rule book it says remove the object after it has been used but under the faqs it says you must re-place the object with a rubble token after it's been destroyed. Is that only when you shoot an object?

Those are two different things. Using an object means using Super Strength or TK to smack someone (or something) with it. If it hits, the object token is removed from the game.

If an object is destroyed by hitting it with 3 clicks of damage (just like a wall can be), then you replace it with a rubble square.