Owing to the chaotic time delay signature (TDS) of chaotic light, there is a "double-peak" phenomenon during the acquisition process of the chaotic Brillouin dynamic grating (BDG) system, which results in inaccurate measurements of the gain and reflection spectra of chaotic BDG systems under temperature variations. This research analyzes the principle behind the appearance of the double-peak in gain and reflection spectra, introduces the ratio of double-peak powers, and investigates the impact of TDS-induced sideband BDG systems on the gain and reflection spectra. The results indicate that the emergence of TDS significantly interferes with the sensing measurements of BDG systems, thereby degrading the measurement accuracy. Experimental results show that by altering the feedback cavity length and feedback strength of the chaotic light feedback loop, the number of sideband BDGs present in the optical fiber can be changed. The relationship between the feedback strength and the ratio of double-peak powers follows a quadratic polynomial rule, and the ratio of double-peak power also alters the influence range of TDS on the measurements. When the feedback strength increases from 0.01 to 0.09, the TDS decreases from 0.441 to 0.095, reducing the influence range of TDS on the gain spectrum by half. Further, the sensing error of the reflection spectrum is reduced to 30 MHz in the temperature range of 35?50 ℃, ensuring the accuracy of chaotic BDG system measurements.