Remove chat is a feature that allows Ops and above to dynamically and instantly remove all previous chat entries from a specific nick from view in the mibbit client and widget. It also removes text from the Recent Chat buffer. This feature will only effect Mibbit client and widget users (if they didn't disable it in prefs). Users accessing your channel from a different IRC client will continue to see the lines that mibbit has removed.
There is no way to recover the text once it is gone. New input from that nick will still be displayed.
Due to the fact that this works based on nick, if a person changes their name and then leaves a message you wish to remove, the messages of the prior nick will not be removed.
If you wish to disable the ability for others to remove chat from your screen, you can tick the preference "General -> Other -> Allow remote chat moderate" off.