Centimeter-sized Te-doped GaSe ingots were grown from the charge compositions of GaSe with nominals 0.05, 0.1, 0.5, 1, and 3 mass% Te, which were identified as ε-GaSe:Te (0.01, 0.07, 0.38, 0.67, and 2.07 mass%) single crystals. The evolution of the absorption peaks of the phonon modes E'(2) (≈ 0.584 THz) and E"(2) (1.77 THz) on Te-doping in GaSe:Te crystals was studied by THz time-domain spectroscopy. This study proposes that the evolution of both E'(2) and E''(2) absorption peaks correlates well with the optical quality of Te-doped GaSe crystals, which was confirmed by experimental results on the efficiency of THz generation by optical rectification. Maximal intensity of the absorption peak of the rigid layer mode E'(2) is proposed as a criterion for identification of optimal Te-doping in GaSe crystals.