A detailed study of the effect of the η-nucleus final state interac-tion (FSI) in the pd→³He η reaction close to threshold is presented.The FSI is incorporated through a T-matrix for η³He elastic scatter-ing, constructed using few body equations. This T-matrix accounts for off-shell and binding effects in η-nucleus scattering. The energy dependence of the data on the   pd→³He η reaction near threshold is reproduced only after including the FSI. The off-shell and binding effects in η³He scattering are found to be important. Given the uncer-tainty in the knowledge of the elementary η-nucleon interaction, the sensitivity of the pd →³He η cross section to different prescriptions of the elementary t-matrix,t_η N→η N is also discussed.