Only moderators have the ability to clear the public chat.
All users in BigBlueButton have the ability to copy the public chat to a clipboard or download the public chat, however, only moderators have the ability to delete the public chat.
To delete the public chat
Expand the Chat Window [1] not already visible, then open the Public Chat Menu [2] located in the upper right of the chat panel.
Select Clear [3] from the list of options.
It is important to note that clearing the public chat cannot be undone and clears all messages from the chat.