When electronic screens are captured by photographic equipment, moiré patterns often emerge due to frequency interference between the camera sensor and the periodic structure of the screen. These artifacts significantly degrade image quality and introduce distinct restoration challenges depending on the image type: natural images require precise color restoration, whereas document images demand high contrast, sharp edges, and structural regularity. To address these issues, we propose the Frequency-Guided Wavelet Transformer (FGWT), a novel framework that leverages frequency decomposition to isolate moiré artifacts across multiple scales and frequencies. Specifically, a recursive Discrete Wavelet Transform (DWT) layer decomposes the image into multi-frequency subbands, which are subsequently refined by a Frequency-Aware Transformer (FAT). FAT enables effective cross-frequency feature interaction and accurate reconstruction of both high- and low-frequency components. Extensive experiments show that FGWT achieves competitive performance, with at least 1.02% and 3.42% improvements in PSNR in the RGB and RAW domains, respectively, compared to leading existing methods. The code is available at https://github.com/howiesssssssssss/FGWT .