Piercing independent sets in graphs without large induced matching

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)≤ω(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).