While I believe the premise of this to be flawed and somewhat black-hat, it is a legit WP question albeit a futile exercise.
You can do something like the following:
#Get the absolute server path to footer.php
$footer_path = locate_template('footer.php');
#Store the footer file contents in a var
$footer_contents = file_get_contents($footer_path);
#The required string
$citation_string = 'Designed by Foo Bar';
#Set off the nuclear bomb if there is an egregious offense
exit('All your websitez are belong to me. Make sure this string "Designed by Foo Bar" is included in footer.php');
I hope you get my tongue-in-cheek innuendoes regarding what a bad user experience this would be. :)
As noted in the comments, there are innumerable ways to route this approach, and any approach for that matter. Anyone can easily reverse engineer any mechanism put in place.