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The processing and recognition of geoscience images have wide applications. Most of existing researches focus on understanding the high-quality geoscience images by assuming that all the images are clear. However, in many real-world cases, the geoscience images might contain occlusions during the image acquisition. This problem actually implies the image inpainting problem in computer vision and multimedia. As far as we know, all the existing image inpainting algorithms learn to repair the occluded regions for a better visualization quality, they are excellent for natural images but not good enough for geoscience images, and they never consider the following gescience task when developing inpainting methods. This paper aims to repair the occluded regions for a better geoscience task performance and advanced visualization quality simultaneously, without changing the current deployed deep learning based geoscience models. Because of the complex context of geoscience images, we propose a coarse-to-fine encoder-decoder network with the help of designed coarse-to-fine adversarial context discriminators to reconstruct the occluded image regions. Due to the limited data of geoscience images, we propose a MaskMix based data augmentation method, which augments inpainting masks instead of augmenting original images, to exploit the limited geoscience image data. The experimental results on three public geoscience datasets for remote sensing scene recognition, cross-view geolocation and semantic segmentation tasks respectively show the effectiveness and accuracy of the proposed method. The code is available at: https://github.com/HMS97/Task-driven-Inpainting.