Crystal symmetry governs the physical properties of materials and provides the framework for interpreting their microscopic excitations and macroscopic responses. In altermagnets, the crystal symmetries that relate opposite-spin sublattices give rise to momentum-dependent spin splitting despite compensated magnetization. Determining the real crystal symmetry is therefore essential for understanding the intrinsic electronic and magnetic properties. For the altermagnetic semiconductor α-MnTe, conflicting Raman assignments have left both its intrinsic lattice excitations and its crystal symmetry unresolved. Here we combine high-resolution Raman and second-harmonic generation (SHG) spectroscopy with first-principles calculations to distinguish intrinsic lattice excitations from Te-derived spectral contributions and to examine bulk inversion symmetry of α-MnTe. We show that several prominent Raman features previously assigned to α-MnTe instead originate from segregated Te clusters or precipitates. The remaining intrinsic Raman response consists of a single Raman-active mode assigned to the calculated E_2g phonon, consistent with the centrosymmetric D₆ₕ symmetry. The SHG response agrees with surface electric-dipole and bulk electric-quadrupole contributions expected for a centrosymmetric D₆ₕ crystal, supporting the preservation of bulk inversion symmetry in α-MnTe. Our findings revise the Raman assignments in α-MnTe and provide a basis for interpreting its altermagnetic properties within the appropriate crystal-symmetry framework.