  The optical potential approach for low-energy scattering of $\eta$-mesons on
three-body nuclei is compared to an exact treatment of the $\eta 3N$ system
using four-body scattering theory with separable interactions in s-waves only.
The higher-order terms including the interaction of the struck nucleon with the
surrounding nuclear medium and virtual target excitations in between successive
$\eta$-scatterings are found to cause important corrections. Effects of final
state interaction in $\eta$-photoproduction on $^3$H and $^3$He are also
studied and sizable contributions beyond the optical model approach are found.
