To recondition the weathered object in the Borrow Some DIY Articles quest, simply click on the paint brush and drag it over the varnish can, then click again.
You will notice a new menu that instructs you to apply two layers.
Click and drag over the weathered object with the paint brush to apply the two layers.
UPDATE: It should take you no more than 30 seconds! If you’re stuck, be sure to cover all areas on the weathered object!