Let's say we have an elliptical orbit that goes from LEO periapsis to apoapsis near Earth's Hill Sphere.
You can merely nudge your satellite at the apoapsis a bit higher (a tiny burn at periapsis), and it becomes Sun's satellite, leaving Earth for a long, long time, moving really slow.
Or you can spend lots of fuel (and energy) to circularize the wide orbit. Then, at any point you can speed up just a little (again, just enough to breach the Hill sphere) and you'll escape the planet - choosing the point and speed right, just at the same speed and in the same direction as in the prior case.
Where did all the energy used to circularize the orbit vanish to?