The topological edge state (TES) may emerge at the interface between acoustic crystals with distinct topological properties. It supports robust wave phenomena against geometry imperfections. By imposing holistic onsite gains and losses in PT symmetric Su-Schrieffer-Heeger lattices, zero mode can be obtained from the convergence of two splitting TES modes induced by adjacent coupling. However, the nonlocal non-Hermiticity requires exorbitant configuration on each atom, resulting in complex systems. Here, we demonstrate the effect of local non-Hermitian modulation to the coupled TESs, utilizing passive acoustic crystals with sandwiched arrangements. Local non-Hermiticity is introduced at the position of one of the TESs to manipulate the splitting TESs. By suitably adjusting the non-Hermitian strength, the splitting TESs experience the coalescence process along with the asymmetric reflection and absorption near and beyond the exceptional point. Due to the topological essentials, the emergence of the exceptional point also can be proved to be robust to the geometrical disorders. Our results reveal that coupled TESs can be modulated by local non-Hermiticity to realize the extraordinary scattering phenomena, which may inspire more acoustic functional devices based on the topological or non-Hermitian characteristics.