What does Montag mean when he says answering the call at the old lady's house is "inconvenient" while pulling down books in the attic in Fahrenheit 451?
Montag exclaims "How inconvenient!" because the woman who owns the books is still in the house when he and the other firemen answer the call.
How inconvenient! Always before it had been like snuffing a candle....The police went first and adhesive-taped the victim's mouth and bandaged him off...so when you arrived you found an empty house. You weren't hurting anyone, you were hurting only things!
Montag is clearly disturbed that the woman, the owner of the books, is still in the house when he and the other firemen arrive. This presence of the woman who owns the books and the house causes Montag discomfiture because he perceives the sordidness of the action of burning someone's home:
She made the empty rooms roar with accusation and shake down a fine dust of guilt that was sucked in their nostrils....
Because this owner of the house is present with all her books, Montag is disturbed, and he feels guilty for his part in the destruction of her possessions. Darkly suggesting what she is going to do, the woman quotes sixteenth British clergyman Hugh Latimer's words to Nicholas Latimer as they were going to be burnt alive for heresy. Like Latimer, the woman is willing to die for what she believes in--her books--and she later does.
In this scene, Montag says "how inconvenient" in response to some books falling on him as he ascends the stairwell to the lady's apartment. To put this into context, we need to look at the next line, in which Montag explains the process of book-burning from a historical perspective. As Montag notes, it was the police's responsibility to arrest a person who was suspected of reading books and then empty his or her residence before the firemen arrived to burn it. Tonight, however, and for reasons unknown, the police have not fulfilled this duty and it is left to Montag and the rest of the crew to deal with the lady and remove the books. For Montag, this is problematic and "inconvenient" because he is confronted with the harsh reality of his job, as he comments in the text:
You weren't hurting anyone, you were hurting only things! And since things really couldn't be hurt, since things felt nothing, and things don't scream or whimper, as this woman might begin to scream and cry out, there was nothing to tease your conscience later.
This foreshadows Montag's impending identity crisis in which he questions the morality of his job and the fireman system as a whole.