We examine the two-photon exchange contribution to the eN --> edelta(1232) --> epiN process with the aim of a precision study of the ratios of electric quadrupole (E2) and Coulomb quadrupole (C2) to the magnetic dipole (M1) gamma*Ndelta transitions. We relate the two-photon exchange amplitude to the N --> delta generalized parton distributions and obtain a quantitative estimate of the two-photon effects. The two-photon exchange corrections to the C2/M1 ratio depend strongly on whether this quantity is obtained from an interference cross section or from the Rosenbluth-type cross sections, in similarity with the elastic, eN --> eN, process.