vinyl plate that the spiral balance is screwed into

I think that I need to buy a couple of window 31" tubular spiral tile window balance red bushing. It is hard to open the window. Does that mean they just need cleaned, or do I need to replace them?

At the top of the tube and behind the tube, where the tube is attached to the window with a screw, do you have the vinyl piece that snaps into the window. I need to order a couple of these balances, or clean them well, but I also need to find out if it comes with, or if I can order the vinyl snap-in piece because while I removed one of the balances, I broke the plastic plate. Without it, I have nothing screw into, and secure the balance to the window. It is just a little piece, but the window won't work without that snap-in plate

I attached a picture with the associated screw. The blue tape is holding the part together.

Thanks,
Rob

I attached a picture of the screw plug. In any case, I think you got the right part. You are amazing