Yashica-Mat LM: What is this part?

Hi ... welcome to the forum!

They are for a "Quick-release" type strap. As you already know, the flat tabs will take any flat type strap which fit through the slots. The QR type straps were used on several makes of TLR.

Do an image search for Yashica mat 124G strap and you will see the quick-release type.