One does not need a TuneIn account to listen to TuneIn radio on an Echo device. It just is there, and any Favorite stations in the Alexa app are only within the Alexa app and can easily be added by the user. Adding stations is easy, but there appears to be no way to arrange them or delete any based upon a Google search
I seem to recall finding a way to delete a station when I first set up my Favorites list, but after trying again today I am stumped.
A while later . . . Since I really want to know the answer, so I called Echo Support. The first assistant could not give me an answer, so she turned my call over to her supervisor who also could not find any answer, and he contacted the higher tier of support and they confirmed there is not a way to delete Favorites in app, but agreed there should be a way and he will suggest this feature be added to the app.