I'm trying to remove the hood ornament emblem on the old grill of my 1980 300TD (so I can install it in a newer grill), which seems to be an easy task, in theory. But when I attempt to twist the brackets (counterclockwise?), it doesn't create any clearance for the unit to pop out. How do I fix this without breaking the thing? Thanks...

you need to pull down on the metal bracket with a pair of channel lock pliers which will rotate it into the position to slide out of the hole. You also might need to squeeze the bracket with the channel locks to make it pop out.

I tried squeezing those outer brackets. But as you can see from the images, they seem too long and they're on the outside of the inner part of the unit.

That is how it comes out. Try squeezing it with channel locks form the side and not from the bottom up.

That star is probably done for. With that much rust its probably going to break apart during removal. Brand new shiny one at the dealer is about $32. I'd just get a new one....

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Pull down on the bracket Don mentioned, and rotate. This should be placed on a "ledge" that sits perpendicular to the brackets. When the bracket has been rotated, it will sit on the ledge and you can pull out the star.

The bracket is what is holding the star to the grille. When you install a new star, you twist this same bracket after inserting the star into position, and it *snaps* into place. You need to perform the reverse of this process to remove the star.

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^^^What he said^^^
It's a strong spring. Be patient. It's also much easier to do if you have the grill out and the plastic insert also removed so you are working with the outer frame of the grill only.
This is also true for when you need to pop that into the new grill.
In my case, I essentially disassembled the spring bracket mechanism and reassembled once out so everything would line back up nicely for the pop back into the new grill. That outer round piece needed to be re-bent into shape.
A vice definitely helps for the re-assembly process if it comes to it.

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