I think it would be nice if you read an inbox notification on the desktop version of the site, it should dismiss the native Android notification in the system tray. It seems kind of weird when I come back to my phone an hour later, and find a bunch of notifications I thought a dealt with... and come to find out I really did deal with them.
This was supposed to be available in an earlier version. Research led me to a deployment issue around the push notification service. It should be fixed now - if you read your inbox on the website it will clear the notification on your android device.