"Rage and then Regret" was an album track from ABC's fourth album, "Alphabet City", which had reached No.7 in the UK album charts.
The decision to go with an album track appears to have been inspired by the group being "between releases" at the time - although the performance would have been filmed before the February 1988 broadcast date, their last single ("King Without a Crown") was released back in November 1987. Their next single, "One Better World", wouldn't be released until May 1988.