Complex sentence: He phones his au pair for his Amex Card; he is keen that she not look into the wrong drawer, but Malcolm snatches the phone and is about to pay when Archie dismisses Anya.
Split into simpler sentences: He phones his "au pair" for a card, keen she not look in the wrong drawer, but Malcolm snatches the phone. He is about to pay when Archie dismisses Anya.