What holds the control to the door...??

That chrome nut.

But......

You appear to be missing the internal keeper, it prevents the barrel of the remote from passing through the door panel.

What I thought... anyone know what it looks like...???

This is one type - www.ebay.com/itm/Mopar-Remote-Mirro...r-GTX-Cuda-Charger-SuperBee/231831641186

Some years used a steel stamped threaded nut.

Edited to add photo, retainer nut at right;

one of my cuda cars I had this ( in the picture ) as a retainer nut to hold it in place,
until you used the screw on nut.

However, on another cuda car I had something like a slip on retainer nut like a letter 'U' shape
snap to push on clip.