Single image reflection separation aims to separate the transmission and reflection layers from a mixed image. Existing methods typically combine general priors from pre-trained models with task-specific priors such as text prompts and reflection detection. However, the transmission prior, as the most direct task-specific prior for the target transmission layer, has not been effectively modeled or fully utilized, limiting performance in complex scenarios. To address this issue, we propose a dual-prior interaction framework based on lightweight transmission prior generation and effective prior fusion. First, we design a Local Linear Correction Network (LLCN) that finetunes pre-trained models based on the physical constraint T=SI+B, where S and B represent pixel-wise and channel-wise scaling and bias transformations. LLCN efficiently generates high-quality transmission priors with minimal parameters. Second, we construct a Dual-Prior Interaction Transformer (DPIT) that employs a dual-stream channel reorganization attention mechanism. By reorganizing features from general and transmission priors for attention computation, DPIT achieves deep fusion of both priors, fully exploiting their complementary information. Experimental results on multiple benchmark datasets demonstrate that the proposed method achieves state-of-the-art performance.