Low Gain Avalanche Detectors (LGAD) for the High-Granularity Timing Detector (HGTD) are crucial in reducing pileups in the High-Luminosity Large Hadron Collider. Numerous studies have been conducted on the bulk irradiation damage of LGADs. However, few studies have been carried out on the surface irradiation damage of LGAD sensors with shallow carbon implantation. In this paper, the IHEP-IME LGADs with shallow carbon implantation were irradiated up to 2 MGy using gamma irradiation to investigate surface damage. Important characteristic parameters, including leakage currents, breakdown voltage (BV), inter-pad resistances, and capacitances, were tested before and after irradiation. The results showed that the leakage current and BV increased after irradiation, whereas overall inter-pad resistance exhibited minimal change and remained above 109 Ω before and after irradiation. Capacitance was found to be less than 4.5 pF with a slight decrease in the gain layer depletion voltage (V
gl
) after irradiation. No parameter affected by the inter-pad separation was observed before and after irradiation. All characteristic parameters meet the requirements of HGTD, and this design can be used to further optimization.