This paper investigates influence of the linewidth enhancement factor on the output of 980-InGaAs/InP fiber grating lasers operating under strong optical feedback. The study is based on intensive numerical integration of an improved time-delay rate equations of semiconductor lasers over wide ranges of the linewidth enhancement factor and ratio of the grating reflectivity to that of the anti-reflecting front facet. The results show that the laser operates in continuous wave and pulsation at small values of the linewidth enhancement factor. Under large values of the factor, the laser happens to exhibits chaos and pulsation. However, such pulsation is predicted to be more stable due to locking of the laser oscillation at the external cavity resonance frequency