Miss White, who went to school with the Bain children, and "knew the girls", said the jokes were not funny.
"These were very offensive and denigrated their memory in the public eye."
Other viewers registered their disgust on the show's Facebook page, but those comments were later removed.
A MediaWorks spokeswoman confirmed the broadcaster had "received a complaint about last Friday's 7 Days programme".
The broadcaster has 20 working days to reply, saying whether a complaint has been upheld. Complainants are referred to the Broadcasting Standards Authority if they are not satisfied with the decision.
The cast of 7 Days