We study ionization of aligned H2+ in strong elliptically polarized laser fields numerically and analytically. The calculated offset angle in photoelectron momentum distribution is several degrees larger for the molecule than a model atom with similar ionization potential at diverse laser parameters. Using a strong-field model that considers the properties of multi-center and single-center Coulomb potentials, we are able to quantitatively reproduce this angle difference between the molecule and the atom. Further analyses based on this model show that the response time of electron to light which is encoded in the offset angle and is manifested as the time spent in tunneling ionization, is about 15 attoseconds longer for the molecule than the atom. This time difference is further enlarged when increasing the internuclear distance of the molecule.