Time series forecasting is critical for demand prediction and resource management in modern Web services, yet applying pretrained Time Series Foundation Models (TSFMs) to downstream tasks remains challenging due to domain shifts. Existing retrieval-augmented approaches typically retrieve coarse-grained window contexts and may introduce context-specific noise.

To address this problem, we argue that temporal patterns should be reused at a decomposition level, as effective trend and seasonal dynamics may originate from different contexts. We propose \method, a two-stage \underline{F}ine-grained \underline{K}nowledge \underline{A}ugmentation framework that decouples and consolidates pre-training knowledge into compact, task-shared residual codebooks to enhance frozen TSFMs.

Specifically, Stage I constructs dual-branch residual codebooks for decoupled trend and seasonal signals, while Stage II dynamically retrieves and merges these fine-grained patterns into target representations via task-adaptive aggregation and gate fusion. Extensive experiments across eight real-world benchmarks with four representative TSFM backbones demonstrate the superior effectiveness and computational efficiency of \method, while further validating the strong transferability of the residual codebooks across different backbones.

The source code is available at the anonymous repository: https://github.com/yuppielqx/TSFM-Component-Token-Adapter