Auto remove white background and add alpha channel to images?
I think you will need something like https://www.drupal.org/project/imagecache_actions if this is in fact not a CSS border added to the image. I would definitely check that first but the above module does do some alpha blending and you can also run your own PHP/GD code during an image cache action so if they don't include it you can find code that does and run that code to perform the change. 

You could also put a border around the image with CSS that would separate the image from the site background to solve something like that.