I don't have this in C# but in PHP, but you can take a look and adaptate to C#.
http://www.havenard.110mb.com/fotomagica/
This is my site where there's a tool to modify the EXIF data of a JPEG and build "magic pictures" which display something in the thumbnail which is not the real picture.
It opens the JPEG, slice its sectors, and build it back ignoring irrelevant sectors and placing my custom made EXIF header.
And this is the source of the PHP classes:
http://www.havenard.110mb.com/fotomagica/class.JpegMapper.php.txt (ExifMapper is incomplete)
http://www.havenard.110mb.com/fotomagica/class.DataMapper.php.txt
You can study it and rebuild in C#, it is really simple to slice a JPEG as you will see.
Usage of this PHP class (only JpegMapper):
$jpg = new JpegMapper('picture.jpg');
$jpg->save_filtered('filtere picture.jpg'); // save removing irrelevant sectors
It is great to get any JPEG even smaller (sometimes a lot smaller).