Wondering what piece this is called.

Thanks for posting! The hardware you have pictured here is the pivot shoe used in a coil balance assembly. Although, it is hard to make out exactly which one you have. I am confident we can supply you with the replacements you need, but I'll need to see an unobstructed photo of it to be able to identify it.

Take a look at the video tutorials, tagged below, for an idea on how to replace your coil balance assembly.

Please feel free to reach out with any questions you might have.