enquiringly: adverb – in an inquiring manner
From the story “Metamorphosis” by Franz Kafka. “Mr. and Mrs. Samsa sat upright there in their marriage bed and had to make an effort to get over the shock caused by the cleaner before they could grasp what she was saying. But then, each from his own side, they hurried out of bed. Mr. Samsa threw the blanket over his shoulders, Mrs. Samsa just came out in her nightdress; and that is how they went into Gregor’s room. On the way they opened the door to the living room where Grete had been sleeping since the three gentlemen had moved in; she was fully dressed as if she had never been asleep, and the paleness of her face seemed to confirm this. “Dead?”, asked Mrs. Samsa, looking at the charwoman enquiringly, even though she could have checked for herself and could have known it even without checking.” (Section III -counting backward paragraph 8).
Now I understand that Mrs.Samsa is asking Grete in a suspecting tone if Gregor is dead, although she can see he is.