Conversations are strictly private, you are the only one who has access to them with your interlocutors, therefore even the administrators of your community do not have access to them.
You can delete your own messages on conversations. The messages will be deleted for you and your contact.
You can also delete an entire conversation. It will then be deleted for you and your contact as well.
Delete a message
First, click on the Messages icon at the top left.
Hover over the message you want to delete, then click the Trash icon.
A new window opens. Press Yes .
Delete a conversation
Click on the cog to the right of the conversation name.
Then click on Delete conversation .
So, do you have things to hide?