  We revisit the process $e^+e^- \to \gamma Z$ at the ILC with transverse beam
polarization in the presence of anomalous CP-violating $\gamma Z Z$ coupling
$\lambda_1$ and $\gamma \gamma Z$ coupling $\lambda_2$. We point out that if
the final-state spins are resolved, then it becomes possible to fingerprint the
anomalous coupling {\rm Re}$\lambda_1$.90% confidence level limit on {\rm
Re}$\lambda_1$ achievable at ILC with center-of-mass energy of 500 GeV or 800
GeV with realistic initial beam polarization and integrated luminosity is of
the order of few times of $10^{-2}$ when the helicity of $Z$ is used and
$10^{-3}$ when the helicity of $\gamma$ is used. The resulting corrections at
quadratic order to the cross section and its influence on these limits are also
evaluated and are shown to be small. The benefits of such polarization
programmes at the ILC are compared and contrasted for the process at hand. We
also discuss possible methods by which one can isolate events with a definite
helicity for one of the final-state particles.
