  We studied the $e^+e^- \to h \gamma$ process at the full simulation level,
using a realistic detector model to study the feasibility to constrain the SM
effective field theory (SMEFT) $h \gamma Z$ coefficient, $\zeta_{AZ}$, at the
ILC. Assuming International Large Detector (ILD) operating at 250 GeV ILC, it
is shown that the $e^+e^- \to h\gamma$ process is much more difficult to
observe than naively expected if there is no BSM contribution. We thus put
upper limits on the cross section of this process. The expected combined 95%
C.L. upper limits for full polarisations $(P_{e^-}, P_{e^+})=(-100\%, +100\%)$
and $(+100\%, -100\%)$ are $\frac{\sigma_{h \gamma}^{L}}{\sigma_{S M}^{L}}<5.0$
and $\frac{\sigma_{h \gamma}^{R}}{\sigma_{S M}^{R}}<61.9$, respectively. The
resultant 95% C.L. limit on $\zeta_{AZ}$ is $-0.020<\zeta_{A Z}<0.003$.
