Hello Mark,
Thanks for getting in touch!
You are at the right place. Sorry about the waiting time, we are a bit overloaded at the moment, so response times are a bit longer. Nonetheless, we do reply to every request.
Just want to notify you upfront that based on our support policy we are limited in supporting customizations. I can give you some pointers and tips to get started but you will need to do the heavy lifting yourself.
It is possible to modify the list view. The easiest would be for that is doing a template override. You can read more details on how you can achieve that in our Themer’s Guide – https://theeventscalendar.com/knowledgebase/themers-guide/
You will likely need to create an override for this file:
wp-content\plugins\the-events-calendar\src\views\list\single-event.php
You will need to figure a way on how to mark an event as being sponsored. Probably using categories or tags would be the simplest. So when the event data is being pulled you check if it is in the ‘sponsored’ category and then put the logo there. Otherwise not.
Hope this helps you get started. Let me know if you have further questions.
Cheers,
Andras