The polarized Raman-scattering spectra of nonsuperconducting α-FeTe and of As-free superconductor Fe1.03Se0.3Te0.7 are measured at room temperature on single crystals. The phonon modes are assigned by combining symmetry analysis with first-principles calculations. In the parent compound α-FeTe, the A1g mode of the Te atom and the B1g mode of the Fe atom are observed clearly, while in superconducting Fe1.03Se0.3Te0.7, only a softened Fe B1g mode can be seen. No electron-phonon coupling feature can be distinguished in the spectra of the two samples. By contrast, the spectra of the superconducting system show a slight enhancement below 300 cm−1, which may be of electronic origin.