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...

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.