  We investigate the sensitivity to the effective operators describing
interactions between dark matter particles and photons at future high energy
$e^+e^-$ colliders via the $\gamma+ \slashed{E}$ channel. Such operators could
be useful to interpret the potential gamma-ray line signature observed by the
Fermi-LAT. We find that these operators can be further tested at $e^+ e^-$
colliders by using either unpolarized or polarized beams. We also derive a
general unitarity condition for $2 \to n$ processes and apply it to the dark
matter production process $e^+e^-\to\chi\chi\gamma$.
