Truth hardware insert
Thanks for reaching out! The piece that has become stripped from your operator base is the worm gear. The 39-339 insert connector is not intended to be used for it. That piece is more so an adapter to be used with the items in the related products.
When the operators become stripped in this manner, they cannot be repaired without heavy machinery. We can provide you with a replacement recommendation for them but I'll need to see a photo of the entire operator.
You'll need to open the window (or a similar window) to obtain the photo. I am specifically looking to see photo of the operator arm(s) and how the mechanism attaches to the bottom of the swinging window sash.
Please feel free to reach out with any questions!