Ionization energy of C2-, C2, and C2+
Bond order has to do nothing with ionization energy, it is the bond dissociation energy which has to be dealt with bond order. For minimum ionization energy, the electron has to be lost from the highest energetic orbital (outer).

In $\ce{C2^-}$, the electron is lost from high energetic $\sigma(\ce{2p_x})$ (if you take the bonding along x-axis) orbital, whereas, in the other two molecules electrons are lost from low energetic  $\pi(\ce{2p_y})$ or $\pi (\ce{2p_z})$ orbitals. So $E_{\infty} - E_\text{initial}$ is higher for the latter case, which makes $\ce {C2^-}$ having lower ionization energy.