According to Urban Dictionary back to school necklace stands for "Noose". The reason for this is that you feel complete despair when school starts up again. For example -

1. I am thinking about that back-to-school necklace.

2. Can't wait to get a back-to-school necklace.

3. That back-to-school necklace is calling me.

For more read - https://astrotonight.com/back-to-school-necklace-meaning/