  We give Bennequin-Plamenevskaya-Shumakovich type lower bounds for the
concordance invariant $s^{\#}$ introduced by Kronheimer and Mrowka. The proof
is a consequence of computations for torus knots and the cobordism inequality
of $s^{\#}$ due to Gong, combined with well-known arguments used for
slice-torus invariants.
