As others pointed out, to extract "gravitational energy" you need to let something fall down, just as in an hydroelectric dam energy is harvested by letting water fall. As the question of what to let fall arises, I suggest to use a couple of Jovian moons.
The solution is quite simple, although there are a few practical problems I let to you to solve - I'm sure by the time you get to Jupiter you will have solved them.
First of all you need a pair of long light and strong tethers - a few millions of kilometres should be enough.
Then you need to attach an end of each tether to a different Jovian moon. Any couple of moons could work.
Attach the other end of the tethers to a sheave with an spring, similar of the device used in extensible cords (example). Keep in mind that the sheave and the spring need to be capable to allocate most of the length of the tethers, but I'm sure that if you have managed to get the tether that won't be a practical concern.
Now you just need to attach an electrical generator to the sheave and you will get plenty of energy that you will webe getting from the mechanical energy of a couple of Jupiter moons. Since you will be braking and accelerating them, they are likely to end falling to Jupiter or getting in the same orbit, but don't worry: there is plenty of moons around to keep powering your house.
You might be concerned by the risk of the tethers getting entangled in Jupiter, but we shouldn't worry about that. If it happens - and if Jupiter surface isn't slippery enough to the tether to free itself - the planet will start pulling the moons and you will get even more energy from Jupiter's rotation. You just need to make sure that the tethers are strong enough and firmly attached to the moons.