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The emblem is attached by two pegs (center left and and center right of emblem's backside) inserted through two holes in the speaker grille. With the speaker grille off, you can push the pegs out of their holes from behind. I'd say that's the safer way to pop out the emblem without scratching up the speaker grille.
The shortcut but slightly more reckless way is to pry the emblem off without removing the grille. I originally pried it off with a plastic pry tool but that marred the rubber along the bottom edge with indentations (examples below).
So I bought a new grille ($50 black plastic for my 1LT but almost $200 aluminum if 2LT/3LT) to clean it up and do it right the second time by popping the grille off its four clips first.
Instead of a pry tool for the shortcut method, you could try sliding fishing wire behind each of the emblem's bottom left/right corners then pull straight out so nothing touches your speaker grille and damages it when you pull. But when you pull, that could embed slash marks into your emblem (won't matter if you trash it). Or if you can figure a way to slide your fingers between the emblem and grille without scratching the grille, you'd have enough leverage to pull it off.
Designer Imagines A Corvette That Looks More Like a Corvette Than the Corvette
Slideshow: A Jaguar designer's personal project imagines what a modern front-engined Corvette might look like if Chevrolet revisited the golden age of the Stingray.
