The way that QuickBooks Self Employed stores customer information is unlike our normal QuickBooks Online or QuickBooks Desktop products. You don't have access to a customer list, rather you just choose the customer from the drop-down on your sales forms. That being said, there isn't a way to remove a customer at this time. I see how this would be useful to businesses like yours and we love hearing your feedback, as it's what helps us grow and create a better product. I'll pass along this idea to our Development Team for possible implementation in the future.
I also noticed this is your first post in the Community, so I'd like to provide you with a super great resource that you can use to stay up-to-date on all things QuickBooks: Our Blog. It's jam-packed full of content and we share new features added to our products often, so I definitely recommend checking it out.
If you have any other questions for me, I'm just a reply away. Have a great rest of your evening!