Hi Justin,
Thanks for reaching out–happy to point you in the right direction here! Nearly all of our plugin templates are structured to be easily modified by the end user, and you’ll find more information on how to get started with making these changes on our Themer’s Guide. For the event hover tooltip, you’ll find the template file to duplicate and modify at /wp-content/plugins/the-events-calendar/src/views/month/tooltip.php.
Our team member Nico provided some great information on modifying event tooltips on another forum thread, which you may also find helpful as you’re getting started here!
Altering Event Tooltip display / displaying Additional Fields in tooltips
I hope these resources help you to make the necessary changes to your site! 🙂 Thanks again for getting in touch, and let us know if you should have any other questions!