We are not using Adobe Target, but the integrated Target from AEM.
The Classic UI is empty there, but I am only able to select the Audiences in order to edit, but there is no way to delete it from the interface, except, of course, if I go to the CRX, but I need to provide to the author users a guide to do it in Touch UI.
I have this question for me as well when I was proposing the solution to you then. And not just this, how will the integration work when we cannot connect AEM with Target Classic (as right now to do things from AEM interface need to connect with target classic).
I would recommend the best way to do things are by using Target Standard vis DTM  .