In Thomas's wonderful code snippet below, the second parameter needs to be changed to "$filename", otherwise the script has no write the file. So the code should read:

<?php
//This function removes all header data from a JPG
function remove_XMP($image_in, $filename) {
  $filename_in = addslashes($image_in);
  list($width, $height) = getimagesize($filename_in);
  $image_dest = imagecreatetruecolor($width, $height);
  $image = imagecreatefromjpeg($filename_in);
  imagecopyresampled($image_dest, $image, 0, 0, 0, 0,  $width, $height,$width, $height);
  imagejpeg($image_dest, $filename);
}
?>