Advanced AI-Generated Content (AIGC) technologies have injected new impetus into teleoperation, further enhancing its security and efficiency. Edge AIGC networks have been introduced to meet the stringent low-latency requirements of teleoperation. However, the inherent uncertainty of AIGC service quality and the need to incentivize AIGC service providers (ASPs) make the design of a robust incentive mechanism essential. This design is particularly challenging due to both uncertainty and information asymmetry, as teleoperators have limited knowledge of the remaining resource capacities of ASPs. To this end, we propose a distributionally robust optimization (DRO)-based contract theory to design robust reward schemes for AIGC task offloading. Notably, our work extends the contract theory by integrating DRO, addressing the fundamental challenge of contract design under uncertainty. In this paper, contract theory is employed to model the information asymmetry, while DRO is utilized to capture the uncertainty in AIGC service quality. Given the inherent complexity of the original DRO-based contract theory problem, we reformulate it into an equivalent, tractable bi-level optimization problem. To efficiently solve this problem, we develop a Block Coordinate Descent (BCD)-based algorithm to derive robust reward schemes. Simulation results on our unity-based teleoperation platform demonstrate that the proposed method improves teleoperator utility by 2.7\% to 10.74\% under varying degrees of AIGC service quality shifts and increases ASP utility by 60.02\% compared to the SOTA method, i.e., Deep Reinforcement Learning (DRL)-based contract theory. The code and data are publicly available at https://github.com/Zijun0819/DRO-Contract-Theory.