There are well-known techniques to clean JPEG artifacts, but they need the tables from inside the JPEG to work best.
Since JPEG uses an 8x8 block transform, you can find artifacts by shifting the image a few pixels over and looking for how the transformed block changes, basically.
Also, using a better chroma upscale can help for small images. libjpeg just uses nearest-neighbor (no "real" resizing) and hardly anyone notices, but it helps with lines and edges.
