The frequency chirp of a self-injected quantum dot (QD) semiconductor laser is studied through the chirp-to-power ratio. By taking into account the carrier dynamics in the nanostructures, the effects of the optical feedback conditions as well as of the linewidth enhancement factor are investigated with a semi-analytical rate equation model. On the one hand, under the long delay case, the simulations show the occurrence of a detrimental parasitic ripple both in the amplitude and the frequency responses. On the other hand, in the short cavity regime, the calculations reveal that the modulation properties can be nicely purified regarding the amplitude and the phase of the delayed field. To this end, substantial improvements in terms of the modulation bandwidth, the relaxation frequency and the frequency chirp are pointed out. Finally, the simulations also show that the linewidth enhancement factor constitutes a severe constraint in the self-injected QD lasers independent of the cavity regime.