Technically there is no way to find out if someone has a website link to yours if you don’t have traffic from your website or if you are looking at their website.
Best would be:
A script that is written every time they refer to your image. It's simple enough by mixing PHP and .htaccess
.htaccess:
RewriteRule path/to/myImage.jpg path/to/myScript.php
myScript.php:
header("Content-type: image/jpeg");
echo file_get_contents("path/to/myImage.jpg");
script, - X // HTML . , script. crontab
myScript.php:
$html = file_get_contents("http://www.theirsite.com");
if(strpos($html, 'path/to/myImage.jpg') !== FALSE)
else