Recently, Belle II reported on the first measurement of $B(B^{\pm }\to K^{\pm }\nu \overline{\nu })$ which appears to be almost 3σ larger than predicted in the Standard Model. We point out the important correlation with $B(B\to K^{⁎}\nu \overline{\nu })$ so that the measurement of that decay mode could help restrain the possible options for building the model of New Physics. We interpret this new experimental result in terms of physics beyond the Standard Model by using SMEFT and find that a scenario with coupling only to τ can accommodate the current experimental constraints but fails in getting a desired $R_{D^{(⁎)}}^{\exp }/R_{D^{(⁎)}}^{\mathrm{SM}}$, unless one turns the other SMEFT operators that are not related to $b\to s\ell \ell$ or/and $b\to s\nu \nu$.