It has been widely investigated for images taken through glass to remove unwanted reflections in deep learning. However, none of these methods have bad effects, but they all remove reflections in specific situations, and validate the results with their own datasets, e.g., several local places with strong reflections. These limitations will result in situations where real reflections in the world cannot be effectively eliminated. In this study, a novel Translation-invariant Context-retentive Wavelet Reflection Removal Network is proposed to address this issue. In addition to context and background, low-frequency sub-images still have a small amount of reflections. To enable background context retention and reflection removal, the low-frequency sub-images at each level are performed on the Context Retention Subnetwork (CRSn) after wavelet transform. Novel context level blending and inverse wavelet transform are proposed to remove reflections in low frequencies and retain background context recursively, which is of great help in restoring clean images. High-frequency sub-images with reflections are performed on the Detail-enhanced Reflection layer removal Subnetwork to complete reflection removal. In addition, in order to further separate the reflection layer and the transmission layer better, we also propose Detail-enhanced Reflection Information Transmission, through which the extracted features of reflection layer in high-frequency images can help the CRSn effectively separate the transmission layer and the reflection layer, so as to achieve the effects of removing reflection. The quantitative and visual experimental results on benchmark datasets demonstrate that the proposed method performs better than the state-of-the-art approaches.