When I'm notified about replies to my posts in the CB nodelet, a checkbox appears to the left of each entry. I generally go to my message inbox and do operations on this messages there. Now, I have tried pressing the only obvious button on the nodelet i.e. "talk" and I have noticed that they're deleted, which seems sensible after all. Still I find it somewhat counterintuitive. Whatever... I wonder if there's more to it: I checked
Chatterbox FAQ and it doesn't seem to me anything really relevant is listed there...