We investigate in the simplest compact D = 4 N = 1 type-II B orientifold models the sigma-model symmetry suggested by the proposed duality of these models to heterotic orbifold vacua. This symmetry is known to be present at the classical level, and is associated to a composite connection involving untwisted moduli in the low-energy supergravity theory. In order to study possible anomalies arising at the quantum level, we compute potentially anomalous one-loop amplitudes involving gluons, gravitons and composite connections. We argue that the effective vertex operator associated to the composite connection has the same form as that for a geometric deformation of the orbifold. Assuming this, we are able to compute the complete anomaly polynomial, and find that all the anomalies are canceled through a Green-Schwarz mechanism mediated by twisted RR axions, as previously conjectured. Some questions about the field theory interpretation of our results remain open.