Numerical results for single-drop exterior mass transport of a solute from a surfactant covered drop to the continuous phase are presented. In particular the effect of physicochemical surface blocking is determined by considering the case in which the adsorbed surfactant accumulates at the rear of the translating drop. The stagnant cap velocity profiles are used to describe convective transport. Surface blocking is incorporated through the choice of a zero flux boundary condition on those portions of the drop where surfactant is present. Finite element numerical results for the Sherwood numbers as a function of Peclet number (Pe ⩽ 104) and stagnant cap angle, φ, show that for surface coverages greater than 0.1π, the effect of surface blocking cannot be ignored. For a Peclet number equal to 104 and φ = 0.5π, the mass transfer coefficients calculated under the assumption that the presence of surfactant reduced convection in the vicinity of the drop without inhibiting the interfacial transport of solute, are found to overestimate the rate of solute mass transfer by as much as 20%.