"la" is a pronoun that works as a direct object, for example "La conosco" means "I know her" (it specifies the object of the verb "conoscere", who he knows) while "le" is an indirect object that means "to her" (it has nothing to do with "le" that means "them", it's only spelled in the same way).

In this sentence "le" doesn't refer to what he is asking (the question)  but to who he is asking to (l'impiegata).