Metasurface inverse design has become central to realizing complex optical functionality, yet translating target responses into executable, solver-compatible workflows still demands specialized expertise in computational electromagnetics and solver-specific software engineering. Recent large language models (LLMs) offer a complementary route to reducing this workflow-construction burden, but existing language-driven systems remain largely session-bounded and do not preserve reusable workflow knowledge across inverse-design tasks. We present an agentic framework for metasurface inverse design that addresses this limitation through context-level skill evolution. The framework couples a coding agent, evolving skill artifacts, and a deterministic evaluator grounded in physical simulation so that solver-specific strategies can be iteratively refined across tasks without modifying model weights or the underlying physics solver. We evaluate the framework on a benchmark spanning multiple metasurface inverse-design task types, with separate training-aligned and held-out task families. Evolved skills raise in-distribution task success from 38% to 74%, increase criteria pass fraction from 0.510 to 0.870, and reduce average attempts from 4.10 to 2.30. On held-out task families, binary success changes only marginally, but improvements in best margin together with shifts in error composition and agent behavior indicate partial transfer of workflow knowledge. These results suggest that the main value of skill evolution lies in accumulating reusable solver-specific expertise around reliable computational engines, thereby offering a practical path toward more autonomous and accessible metasurface inverse-design workflows.