2008 Solstice Base. I completed the project today.
To remove/ replace the emblem you have to take the bumper off. Here's how I did it.
I put the car up on ramps; it makes it easier to get underneath to pull out the plastic fasteners.
First, I removed the 7mm bolts along the top. Don't forget the corner where the side marker lights bolt up.
Second, I removed the 7 mm bolts from the fender well to the bumper.
Third, I went underneath and popped out the plastic fasteners. The local True Value had a decent selection of plastic auto fasteners back where they sell single fasteners.
Fourth, I removed the 10mm bolts that hold the fascia/bumper to the frame.
At this point there is nothing holding it on. Now it's just a matter of wiggling it the right way to get it loose at the corners. Once you do that it will come off in your hands. Don't fear. It is super light and mine rested very nicely in place without anything holding it. This is when I found it the easiest to pull out the bulbs for the signals, fog, and side markers. Once I had the bumper off, I had the wife come out to the garage, and hold the bumper up in the air while I pulled the bulbs.
The emblem is on with speed nuts. Be careful putting the new one on. The speed nuts cut threads on the plastic posts as you crank down. Crank too far, and you'll snap one. Ask me how I know that.
It was easy to put the bumper back on. Just do the assembly in reverse starting with the 7mm bolts on the top. Put everything back together, but do not tighten anything up until everything lines up. I did it by myself (no help from the wife), in about an hour.