Buttondown uses Amazon S3 (a fairly common file hosting platform) to safely and securely store your images. They last indefinitely by default; there's no interface to delete images that you've uploaded to Buttondown, but you can do so via the API (or email me and I can manually delete them on your behalf.) This means that even if you were to delete the email in which images are referenced, the images themselves still exist on Buttondown's servers.