This is all that is left. How do I remove it?

 

I don't have access to my car right now, but that looks like the covers part of the snap that sheared and stayed on the bottom (?). If so, push it down and pull.

Best!

 

I have a new (to me) cover and can see that that the center is supposed to be pulled up to release. There is almost nothing left but the part I can grab won't pull up!

 

What exactly is that picture of? Car side, cover top, or cover bottom?

 

It is the fastener stuck on the pin at the back of the car. Tomorrow, in the light, I'll take another picture not zoomed in as far.

 

These pictures might help put the first photo into context:
New cover in position but not fastened down. It can't fasten because the old fastener is stuck on the pin.
New cover pulled back showing old fastener on pin.
Old fastener stuck on pin

 

Could you pry it up with a pair of small flat blade screw drivers, or needlenose pliers? Does to rotate in position? If yes, then it's not glued on (Lord knows what the P.O. may have done)

John

 

It will spin but when I grabbed it with pliers it would not pull off. I will try prying tonight it tomorrow.

Judging by the frayed remains of the old cover it appears that it jammed on and couldn't be removed, resulting in the old cover being torn off.
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I think it's a "Tenax" fastener made by GHE.

Can you get a self-tapping screw of the correct size to sort-of screw into the centre just enough to give you enough grip to pull the middle bit upwards. That should release it from the stud which is fixed to the car.

Or ............. just crush the whole lot together with Mole Grips and then unscrew it from the car - complete new fittings are widely available :

TENAX Fasteners "Made In Germany"

 

Thanks! I now know that, worst case, I can unscrew the old stud and get a replacement on eBay or other sources.