When people seek to touch the fringe of Jesus' garment, the detail is not merely decorative. Jewish clothing could include tassels or fringes worn in obedience to biblical instruction.
The same background also explains why Jesus can criticize religious leaders for enlarging their fringes: an ordinary sign of covenant obedience could also become a visible means of displaying piety.
Numbers 15 and Deuteronomy 22 command Israelites to place tassels or fringes on their garments. These served as visible reminders of belonging to Israel and of the obligation to remember God's commandments.
The Gospel references therefore belong to recognizable Jewish dress. The texts do not portray the fringes themselves as objectionable. Jesus' criticism concerns using visible religious markers for public display and status.
Knowing the biblical background keeps the reader from treating the fringe as an exotic costume detail. It was connected with obedience to Torah and Jewish identity.
That makes both kinds of Gospel references more meaningful: sufferers reach toward a recognizable part of Jesus' Jewish clothing, while ostentatious enlargement of the same religious marker can become an example of piety performed to be seen.