Hey Marnie,
No problem.
No, you don’t need to delete the key from the live site to have the files work on the development site. Once the plugin is installed and activated (even without the license key) it should work properly and with full functionality. The license key only gives you access to plugin updates and does not restrict functionality.
If you’re having trouble seeing on the dev site, try downloading a fresh version of the plugin from here and uploading and activating on your site (being sure to also have the core events calendar plugin from WordPress.org active on the site).
Let me know if this helps.
Thanks!