Autonomous Underwater Vehicles (AUVs) play a crucial role in underwater exploration. Vision-based methods offer cost-effective solutions for localization and mapping in the absence of conventional sensors like GPS and LiDAR. However, underwater environments present significant challenges for feature extraction and matching due to image blurring and noise caused by attenuation, scattering, and the interference of \textit{marine snow}. In this paper, we aim to improve the robustness of the feature extraction and matching in the turbid underwater environment using the cross-modal knowledge distillation method that transfers the in-air feature extraction and matching models to underwater settings using synthetic underwater images as the medium. We first propose a novel adaptive GAN-synthesis method to estimate water parameters and underwater noise distribution, to generate environment-specific synthetic underwater images. We then introduce a general knowledge distillation framework compatible with different teacher models. The evaluation of GAN-based synthesis highlights the significance of the new components, i.e. GAN-synthesized noise and forward scattering, in the proposed model. Additionally, VSLAM, as a representative downstream application of feature extraction and matching, is employed on real underwater sequences to validate the effectiveness of the transferred model. Project page: https://github.com/Jinghe-mel/UFEN-GAN.