We propose a deep learning approach for inpainting holes in digital models of fabric surfaces. Leveraging the developable nature of fabric surfaces, we flatten the area surrounding the holes with minor distortion and regularly sample it to obtain a discrete 2D map of the 3D embedding, with an indicator mask outlining holes locations. This enables the use of a standard 2D convolutional neural network to inpaint holes given the 3D positioning of the surface. The provided neural architecture includes an attention mechanism to capture long-range relationships on the surface. Finally, we provide ScarfFolds, a database of folded fabrics patches with varying complexity, which is used to train our convolutional network in a supervised manner. We successfully tested our approach on various examples and illustrated that previous 3D deep learning approaches suffer from several issues when applied to fabrics. Also, our method allows the users to interact with the construction of the inpainted surface. The editing is interactive and supports many tools like vertex grabbing, drape twisting or pinching.