1973 Front bumper mounting hardware

So the state says I have to mount a front licences plate on my car.  I have a new mount bracket and was looking to bolt it on but I cant figure out what is holding my bumper on now.  The pictures below show the bumper on the car looking up.  As you can see the bumper mounting hardware are plastic and are holding the bumper on quite tight.  I tried to pull one off but it isnt budging and I dont want to break it.

Anyone know what these are and how to take them off.  What hardware should I have, hex bolts, philip bolts?

Thanks for any advice.  

That's nothing Ford ever put in there, probably just some modern push in body plugs.

I figured as much, thanks for the drawing too.  I am impressed how tight the bumper is on the car with the plastic push in's.  Ill get one out and send a pic.

Thanks again.

Here is the fastener I just pulled out of the bumper.  No need to pull the other 4 after I get the Liscense bracket installed, they were installed quite securely.  Dimension was 3/8" + wide and about 7/8" tall.  (The line at the 4 is actually the 3/4" and 7/8" on the ruler)

Thanks again for the advice. 

There should be bolts in those holes. Without those bolts the only bolts holding the urathane bumper to the bumper frame would be the small nuts on the front side (inside) of the bumper frame.