It's a Hohmann transfer orbit. It will be orbiting the sun, with a periapsis (point of closest approach) at Earth's orbit an apoapsis at Mars's orbit. It's not going to circularize at Mars, and indeed will intersect Mars orbit quite a ways behind Mars.
The car is on an elliptic heliocentric orbit that crosses the Earth orbit at its perihelion and crosses Mars' orbit at its aphelion. It is not in orbit around either planet.
