Does this device which claims to reduce reactive energy from a house work?
This is mostly a con.  The circuit is probably only to light the LED so that it looks like it's doing something.

Most power grid loads, like your house, are inductive.  Inductive power factor (current lagging voltage) can be offset by adding capacitive power factor (current leading voltage).  If you get it just right, then the result looks resistive, which is the ideal.  At best the box is a capacitor.  At worst, it is a outright scam.

Even if the small box is a genuine capacitor, it doesn't do anything for you.  You are billed by the real power you use, regardless of the reactive component.  At best adding a capacitor on your line is doing the power company a slight favor, but such a small box will have a tiny effect even if it is a real capacitor.

Adding a fixed capacitance to the line blindly offsets some amount of inductance.  That is probably more useful than not to the power company, because on average the load on the power line looks inductive.  It will cancel a tiny amount of inductance you are causing, or if you aren't, a tiny amount of inductance from your neighborhood.

Overall, the current to run the LED causes more waste than anthing useful a capacitor that would fit into the small box can do.  The purpose of this device has nothing to do with power factor.  It's all about gullability factor and separating non-technical people from their money.  Since you have one, it is apparently working as intended.