We numerically investigate the time delay signature (TDS) properties of a chaotic semiconductor laser subject to nonlinearly-modulated feedback. In the proposed scheme, two semiconductor lasers that play the role of a built-in nonlinear modulator is positioned in the external cavity of the chaos generator laser, which forms a structure of semiconductor laser ring. The simulation results show that the TDS of the chaos generator in the laser ring is quite smaller than that of the chaos induced by the conventional optical feedback. Moreover, the TDS embedded in the intensity and phase time-series of the chaotic signal can be further concealed, by introducing an additional optical feedback into the built-in nonlinear modulator.