The origin is rooted in the Mahabharata story of Draupadi and Krishna, along with traditions of tying protective threads and regional festivals on Shravana Purnima.
In the Mahabharata, when Krishna was injured in battle, Draupadi tore a strip from her sari and tied it on his wrist to stop the bleeding. Touched by her care, Krishna vowed to protect her and later shielded her when she was humiliated in the court.
Mahabharata; regional Shravana Purnima tradition