Tone refers to the way the author feels about the subject of the text. It is often confused with mood, which refers to the feeling created within the reader by the text. A easy way to keep them straight is to think about tone as describing the way the author feels and mood as describing how the reader feels.
I would describe the tone of this text as sympathetic, as Faulkner could present Emily Grierson as a total monster, but he, instead, presents her somewhat gently, given what he could do. It seems as though Faulkner sees her behavior as more tragic than monstrous, the result of the fact that she is terrified of being left alone (as she was when her father passed away, and as she seems to fear toward the end of her relationship with Homer Barron). Emily's house is described as being the only one left on her street, "lifting its stubborn and coquettish decay above the cotton wagons and the gasoline pumps——an eyesore among eyesores." It's like her, a relic that no longer fits in, that stands alone and odd in the context of a newer, more modern age. Faulker further humanizes her by making her the subject of pity; when she was left only the house after her father's death, she would have to learn, finally——like everyone else——how to pinch a penny. Emily, however, could not accept her father's death and attempted to retain his body, several days past the time it would have stayed fresh. Such denial seems designed to elicit our sympathies as well, as does the incident regarding the smell emanating from her home, lulling us a bit before the bombshell of Homer's murder.