We compute the contribution of the decays K_L rightarrow pi ^0 Q {bar{Q}} and K^+ rightarrow pi ^+ Q {bar{Q}}, where Q is a dark fermion of the dark sector, to the measured widths for the rare decays K^+rightarrow pi ^+ nu {bar{nu }} and K_Lrightarrow pi ^0 nu {bar{nu }}. The recent experimental limit for varGamma (K^+ rightarrow pi ^+ nu {bar{nu }}) from NA62 sets a new and very strict bound on the dark-sector parameters. A branching ratio for K_L rightarrow pi ^0 Q {bar{Q}} within the reach of the KOTO sensitivity is possible. The Grossman–Nir bound is weakened by the asymmetric effect of the different kinematic cuts enforced by the NA62 and KOTO experiments. This last feature holds true for all models where the decay into invisible states takes place through a light or massless intermediate state.