Isn't "Imperial Royal Guard" redundant? IINM, the group's Japanese name can be translated as "Imperial Guard Knights" (literally) or "Imperial Guard(ians)" (more figuratively).
It’s less redundant, but strictly speaking rather different as royal comes from “rex” and refers to a king.
”Imperial and royal” is technically only used if someone or something has a relation to an emperor
and a king. Like how some members of the Habsburgs (because the emperor of Austria was also king of Bohemia and Hungary) or the crown prince of the German empire (because the German emperors were also kings of Prussia) were addressed as “Imperial and Royal Highness”.
That being said, the imperial guards know how to deal with Conia – by offering her sweets. So we can assume they met her before (aside from the prince)?