An update of the previous OPAL measurement of the inclusive production of charged D*+- mesons in anti-tagged photon-photon collisions is presented using all data collected at e+e- centre-of-mass energies between 192 and 208 GeV. The D* mesons are reconstructed in their decay to D0 pi+ with the D0 observed in the two decay modes K- pi+ and K- pi+ pi- pi+. The cross-section for the anti-tagged process e+e- to e+e- D* X are measured in the restricted kinematical region 2 GeV < pt_D* < 12 GeV and |eta_D*| < 1.5. The measurement is extrapolated to obtain a total anti-tagged charm production cross-section. The differential D* cross-sections as a function of transverse momentum and pseudorapidity are also presented and compared to next-to-leading order (NLO) perturbative QCD calculations.