  We discuss the behavior of head-to-head $e\gamma\to e\gamma$ scattering
process in the noncommutative quantum electrodynamics on the Moyal space amid
its unresolved forward scattering singularity. We model the effect of the
currently unknown resolution to this collinear singularity by cut-offs which
are functions of the control variable $s/\Lambda_{\rm NC}^2$ and find that such
cut-off functions can suppress NC corrections to the inverse Compton scattering
to negligible. We also notice that such cut-offs leave the integral cross
section of the forward region larger than the backward region all the time,
making the former potentially easier to observe. Our estimations indicate that
such an effect may be visible in the future collider experiments when the scale
of noncommutativity $\Lambda_{\rm NC}\gtrsim1$ TeV.
