We propose and demonstrate experimentally the generation of chaos with suppressed time-delay signature (TDS) and physical random bits in two mutually coupled semiconductor lasers (MCSL) by introducing an auxiliary fiber Bragg grating (FBG) filtered injection path. The measurements show that, even by simply adding a single FBG path, the TDS of chaotic signals generated by both lasers in our proposed scheme can be better concealed compared to the conventional MCSL system. Moreover, better TDS concealment can be achieved in the laser with smaller wavelength. Additionally, two random bit streams extracted from the two chaotic lasers in the proposed scheme are achieved with minimal post-processing. The total generation rate reaches 640-Gbps.