Power-to-gas (P2G) can convert excessive renewable energy into hydrogen via electrolysis, which can then be transported by natural gas systems to bypass constrained electricity systems. However, the injection of hydrogen could impact gas security since gas composition fundamentally changes, adversely effecting the combustion, safety and lifespan of appliances. This paper develops a new gas security management scheme for hydrogen injection into natural gas systems produced from excessive wind power. It introduces four gas security indices for the integrated electricity and gas system (IEGS) measuring gas security, considering the coordinated operation of tightly coupled infrastructures. To maintain gas security under an acceptable range, the gas mixture of nitrogen and liquid petroleum gas with hydrogen is adopted to address the gas security violation caused by hydrogen injection. A distributionally robust optimization (DRO) modelled by Kullback-Leibler (KL) divergence-based ambiguity set is applied to flexibly control the robustness to capture wind uncertainty. The KL divergence-based ambiguity set defines uncertainties within a measured space which limits the shape of probability distributions. Case studies illustrate that wind power is maximally utilized and gas mixture is effectively managed, thus improving gas security and performance of IEGS. This work can bring many benefits: i) ensured gas security under hydrogen injection ii) low system operation cost and iii) high renewable energy penetration. It can be easily extended to manage injections of other green gases into IEGS.