1) Use Batch Update Users tool in ACP to find and remove members
2) Go into Inbox, many of those several years old conversations are with those members who are now removed and shown as guests.
3) Select All, and take action Leave Conversation. Nothing changes after that. No conversation is removed. Either Ignore or Accept future conversation option will all lead to the same result.
However, if you go to each individual conversation and chose to Leave Conversation, it will remove that specific conversation.