  We examine Lorentz-violating effects that could appear through deviations of
the Standard Model gauge couplings WWgamma and WWgammagamma. These new physics
effects are explored on the gamma gamma -> WW reaction at the International
Linear Collider. In particular, the associated helicity amplitudes are computed
in the context of the Standard Model Extension (which is a model-independent
approach to CPT and Lorentz violation) and the Effective Lagrangian Model
(which incorporates new physics effects that respect CPT and Lorentz
violation). We perform an exhaustive study of the polarized differential cross
sections to stand out effects related to Lorentz symmetry violation, where it
is evidenced that the effects of Lorentz symmetry violation are more sensitive
to the presence of the b constant background field. We found that for the
$(\pm,\pm,(L,T+T,L))$ polarization state, only Standard Model Extension and
Effective Lagrangian Model contribute at the lowest order, however, both types
of new physics effects are clearly distinguished, being dominant the convoluted
cross section of the Standard Model Extension in around 4 orders of magnitude.
For this polarization state, at the last stage of operation of International
Linear Collider, it is expected an integrated luminosity of 10^3 fb^{-1},
finding around of 2 events for a Lorentz-violating energy scale of 32 TeV.
