Need Help with an 'unconventional' way of setting up a switch 3-way with 12-2

Thank you that makes total sense. I pulled the light down to make the changes and I noticed this component clipped around the two blacks feeding the light. Did some googling and it’s a ferrite core from Wurth Elektronics.]([74271111 Würth Elektronik | Filters | DigiKey])
Here’s a pic of how it’s used:


I assume it’s because there’s no neutral but I’m not sure if I need it now that I’m changing the configuration.

Any ideas?