For a lossless format (except JPEG), your idea is to download it as a bitmap and save it again in order. Not sure if .NET natively supports TIFF (I doubt it is).
For JPEG, as you suggested, there may be a loss of quality if you recompress the file after unpacking it. To do this, you can try ExifLibrary and see if it has anything. If not, there are command line tools (such as ImageMagick) that can strip metadata. (If you use ImageMagick, you are all set up, as it supports all the required formats. The command you want is convert -strip.)
For TIFF.NET has built-in classes TiffBitmapDecoderand ...Encoderthat you could use; see here .
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