Balance Help

I have windows that use block and tackle balanced series 850. I have one window where the balance screw that goes into the frame has had a small square anchor piece come out of the frame. Now there is nothing for me to screw the balance into the frame with. I have the square anchor looking piece but I'm not sure glue will hold it in place. Is there a replacement part for this or should I drill a new hole just below the existing opening of the old screw hole? Thank you

If I buy a new screw plug does it have some sort of tabs, like a wall anchor of sorts, to hold it in place? Or do I use glue? I've included two pics of my existing screw plug. It doesn't look like there is anything to actually keep it in the window frame hole.