In this scene from Fahrenheit 451, it is not the alarm that is "inconvenient" for Montag. Rather, it is the fact that on arriving at the house, the woman is present and able to talk. As Montag explains in the next few lines, it is usual practice for the firemen to arrive after the police. As such, the police have already arrested the victim, "bandage-taped" his or her mouth, and taken the victim to the police station. So, when the firemen arrive, the house is empty and all they have to do is burn the place.
On this occasion, however, Montag arrives to find the victim still in the house. It is "inconvenient," then, that he has to face the old woman, to listen to her side of the story, and therefore to literally confront the realities of his profession.
Usually, before the firemen arrived at the house, the occupants had already been arrested and taken away. However, in this call, Mrs. Blake was still at home. Montag found this inconvenient because it made it more personal. Before it was all about "things," not people. It was simply "janitorial work."
Even worse, Mrs. Blake refused to be taken away. She soaked herself with kerosene, lit a match, and set herself on fire. It affected the entire fire crew. They began to question, if only temporarily, the virtue of their job. For Montag it would be one of the events that eventually lead him to open rebellion.