Actually, the object does have _potential_ energy. I've wondered about OP's question before. I think the answer has to do with the fact that these "teleporters" don't transport matter in the conventional sense.
Suppose you did have have a teleporter that could take an object and teleport it 100 ft up a hill. If you dropped the object, collected the potential energy (like in a waterwheel), and teleported it again, you shouldn't be able to violate conservation of energy or make a perpetual motion machine. So, I figure it's either A) impossible, or B) requires an energy input at _least_ equal to the change in potential energy. \\
Of course, I'm talking about gravitation potential energy, but that's just one field. There's also electromagnetic. Conversely, if it took more energy in than the net change in potential energy, where would that energy go? So I suppose the net energy input should be equal to the change in potential energy. \\
This also raises other issues, like if I teleport very far away, or two a more massive planet, I might need to input a lot of energy on this side. \\
A possible resolution to this problem is that the kind of teleportation here is just informational--that is changing one particle's state to match (or oppose) the one on the other side. Thus no mass (or charge) is transported anywhere, and everything is happy energy-wise.