Graph domain adaptation (GDA) has achieved great attention due to its effectiveness in addressing the domain shift between train and test data. A significant bottleneck in existing graph domain adaptation methods is their reliance on source-domain data, which is often unavailable due to privacy or security concerns. This limitation has driven the development of Test-Time Graph Domain Adaptation (TT-GDA), which aims to transfer knowledge without accessing the source examples. Inspired by the generative power of large language models (LLMs), we introduce a novel framework that reframes TT-GDA as a generative graph restoration problem, "restoring the target graph to its pristine, source-domain-like state". There are two key challenges: (1) We need to construct a reasonable graph restoration process and design an effective encoding scheme that an LLM can understand, bridging the modality gap. (2) We need to devise a mechanism to ensure the restored graph acquires the intrinsic features of the source domain, even without access to the source data. To ensure the effectiveness of graph restoration, we propose GRAIL, that restores the target graph into a state that is well-aligned with the source domain. Specifically, we first compress the node representations into compact latent features and then use a graph diffusion process to model the graph restoration process. Then a quantization module encodes the restored features into discrete tokens. Building on this, an LLM is fine-tuned as a generative restorer to transform a "noisy" target graph into a "native" one. To further improve restoration quality, we introduce a reinforcement learning process guided by specialized alignment and confidence rewards. Extensive experiments demonstrate the effectiveness of our approach across various datasets.