That's sad. What happens when your inbox fills up? At least on the old board, we could delete any PMs that we wanted (especially if we didn't want to have them around).
The new software is full of surprises, still finding new stuff even 10 months later! Try this:
When viewing your list of Conversations (or "inbox" using old terminology)
There should be a little little square between your avatar and the conversation title
Then a pop-up appears and "Leave Conversations..." is one of the options; if for some odd reason the pop-up doesn't appear, you can click on "Selected Conversations:1" in red text at the bottom right of the list and get the same options
You'll then get an option to "Accept Future Message" or "Ignore Future Messages" -- if you Accept, the full thread will return if the other participant(s) replies again; if you Ignore, the other participant would need to start a new Conversation to reply to you again
I believe you can select multiple Conversations at one time if you wish to clear out several (or even all).
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