The researchers identify the watermarks to be removed by finding pixel patterns that persist across a large number of images, as shown on this animation: https://1.bp.blogspot.com/-cJwNoUxIBzM/WZTDpw3ru6I/AAAAAAAAB... . Their proposed solution is to randomly warp the watermarks.

Unfortunately, their solution could be quickly defeated with image-to-image generative adversarial convnets trained to... remove watermarks from image pairs. (That is, instead of training a model to change, say, image style or resolution, train it to remove artificially added watermarks.)