Combination bonuses from main cookie and pet will be carried through the cookie relay. For example, combining Ninja Cookie and Little Ghost will gives "+1,500 points for destroying an obstacle". When Ninja Cookie is out and energy and replaced by Hero Cookie as relay, every points from Hero Cookie will still gives "+1,500 points for destroying an obstacle".
However, combination bonuses from relay cookie and pet combination will not be carried when cookie relay is used. Instead, the original combination bonus from pairing main cookie and pet will be carried over, or no combination bonuses will be affected if the main cookie and pet has no combination bonus.