  The rare decays $B^+\to K^+ \mu\bar \mu$ and $B^0\to K^{*0} \mu\bar\mu$
provide the strongest constraints on the mixing of a light scalar with the
Higgs boson for GeV-scale masses. The constraints sensitively depend on the
branching ratio to muons. Additional decay channels like an invisible partial
width may substantially weaken the constraints. This scenario will be probed at
Belle II in $B\to K^{(*)} + \mathrm{inv}$. We illustrate the complementarity of
scalar decays to muons and invisible decays using the currently available
results of LHCb and BaBar. We provide two simple model realisations providing a
sizeable invisible scalar width, one based on a real scalar and one based on a
$U(1)_{B-L}$ gauge symmetry. In both examples the scalar decays into heavy
neutral leptons which can be motivated by the seesaw mechanism for neutrino
masses.
