Observing the production of the Higgs particle in the γ γ mode of a linear e + e − collider allows for the measurement of the H γ γ coupling. We point out that for the intermediate Higgs mass range this measurement is considerably more challenging than previously believed. The b ¯ b signature receives a large background from the production of heavy quark pairs by resolved photons. We quantify the experimental requirements needed to make a meaningful measurement in the presence of this background.