In this work, via autocorrelation function (ACF) and permutation entropy (PE) methods, we numerically investigate the time-delay signature (TDS) characteristics of the chaotic signal output from an optoelectronic oscillator (OEO) after introducing an extra optical feedback loop. The results demonstrate that, for such a chaotic system, both the optoelectronic feedback with a delay time of T1 and the optical feedback with a delay time of T2 contribute to the TDS of generated chaos. The TDS of the chaotic signal should be evaluated within a large time window including T1 and T2 by the strongest peak in the ACF curve of the chaotic signal, and the strongest peak may locate at near T1 or T2. Through mapping the evolution of the TDS in the parameter space of the optical feedback strength and time, certain optimized parameter regions for achieving a chaotic signal with a relatively weak TDS can be determined.