We present the experimental study of ultrafast optical excitation of surface magnetostatic spin wave (MSSW) packets and their spectral properties in thin films of pure iron. As the packets leave the excitation area and propagate in space, their spectra evolve non-trivially. Particularly, low or high frequency components are suppressed at the border of the excitation area depending on the orientation of the external magnetic field with respect to the magnetocrystolline anisotropy axes of the film. The effect is ascribed to the ultrafast local heating of the film. Further, the time resolution of the implemented all-optical technique allows us to extract the chirp of the MSSW packet in the time domain via wavelet analysis. The chirp is a result of the group velocity dispersion of the MSSW and, thus, is controlled by the film magnetic parameters, magnetization and anisotropy, and external field orientation. The demonstrated tunable modulation of MSSW wave packets with femtosecond laser pulses may find application in future magnonic-photonic hybrid devices for wave-based data processing.