We determine the bosonic part of the superstring sigma model Lagrangian on eta-deformed AdS_5 x S^5, and use it to compute the perturbative world-sheet scattering matrix of bosonic particles of the model. We then compare it with the large string tension limit of the q-deformed S-matrix and find exact agreement. We comment on the structure of the RR sector of the type IIB SUGRA background.