Production of negative strangeness in reactions of inelastic anti-neutrino scattering on a nucleus provides information on the modification of strange degrees of freedom in nuclear matter. We calculate cross-sections of the reaction channelsν e(µ) → e + (µ + ) + K − andν e(µ) + p → Λ + e + (µ + ) and investigate their sensitivity to the medium effects. In particular, we consider effects induced by the presence of a low-energy excitation mode in the K − spectrum, associated with the correlated Λ-particle and proton-hole states, and the renormalization of the weak interaction in medium. In order to avoid double counting, various contributions to anti-neutrino scattering are classified with the help of the optical theorem, formulated within the non-equilibrium Green's function technique.