On the Aridor Slave Rescue game, to un-BG a character is the opposite of to BG a character. It means, getting rid of the bodyguards assigned to a character, so they can be captured by ordinary means. It is used to refer both to situations where a player deliberately gets rid of the bodyguards on their own character (by losing a contest for instance), and where a player rumbles or biobombs another in order to get rid of BGs.
Enigma wanted the Emperor off me so he biobombed me repeatedly to un-BG the character and then stole him.
It's quite easy to un-BG the credit chicks because all you need to do is pick a contest with a strong character to lose them.