  Given a graph $G$, denote by $h(G)$ the smallest size of a subset of $V(G)$
which intersects every maximum independent set of $G$. We prove that any graph
$G$ without induced matching of size $t$ satisfies $h(G)\le
\omega(G)^{3t-3+o(1)}$. This resolves a conjecture of Hajebi, Li and Spirkl
(Hitting all maximum stable sets in $P_{5}$-free graphs, JCTB 2024).
