The blow-dryer attachment that stretches and softens textured hair and loosens the curl pattern is a:

The blow-dryer attachment that stretches and softens textured hair while loosening the curl pattern is the pick nozzle. This attachment is specifically designed to gently lift and separate the hair strands while applying heat, which helps in elongating the curl pattern without causing excessive frizz. The shape of the pick nozzle, with its wide, spaced prongs, allows for better airflow and makes it easier to work through textured hair, maximizing the desired results.

Other attachments like the concentrator direct heat but do not aid in stretching curls, while a diffuser is meant to distribute heat evenly to maintain curl definition rather than loosen it. Butterfly clips are not attachments for blow-dryers at all but are tools used for sectioning hair during styling. Understanding the purpose and functionality of these tools is crucial for effective hair styling, especially with textured hair.