Delete on v3 and the apps isn't available. As far as I know that hasn't been there since the start of v3, which the apps got first.
Not sure if they are going to add that in the future or not. But until then you can archive to get them out of your inbox.
With the new update to the iPhone app, I can swipe the messages to the left to find an "archive" option, but I don't see any way to delete them. Is there no way to do this? Thanks for any feedback.