It would depend on how the theme’s templates normally get the featured image URL. There’s a good chance the_post_thumbnail_url() or something closely related is used. In that case you can alter the URL returned with the ‘wp_get_attachment_image_src’ filter. Your callback is passed several bits of data (see the source for more info in the inline docs), and your callback returns an array that includes the URL, width, and height. You may return whatever is appropriate in your case here, and the data will be used in building the featured image HTML.
If you’re not familiar with using filters, it’s worth learning about because filters (along with closely related “actions”) are the primary way we alter the way WP works. You might start with Plugin API. The concept applies even if you are not making a plugin.
A simple plugin is a viable option, you can use it to contain other code tweaks that you might come up with. You can also place code on your theme’s functions.php file, but your changes will be overwritten when the theme updates. To protect your code, create a child theme or create a plugin. Either option is easy to accomplish, how-tos are all in the Codex. If something is not making sense, come back here and someone should be able to set you straight.
