  The littlest Higgs model with T-parity (LHT) has new flavor-changing (FC)
couplings with the Standard Model (SM) quarks, which do not suffer strong
constraints from electroweak precision data. So these FC interactions may
enhance the cross sections of some flavor-changing neutral-current (FCNC)
processes. In this work, we study the FC top-charm associated productions via
$e^{-}\gamma$ collision at the ILC. We find that the cross sections are
sensitive to the mirror quark masses. With reasonable values of the parameters,
the cross sections may reach the detectable level and provide useful
information about the relevant parameters in the LHT model, especially setting
an upper limit on the mirror quark masses.
