You talking about the vent immediately to the right of the audio unit? That panel only has a few clips holding it in. Just pry it off carefully. The 12V accessory socket connector has a small tab that needs to be depressed to disconnect it.
I definitely suggest investing in trim panel removal tools like this: Trim And Molding Tool Set, 5 Pc.
And take the time before you pull it apart to get the replacement vent. She wont like driving around in a car that looks like its falling apart!
First you need to pop off the trim panel to right of the audio unit.- the one that has one of the round vents and the 12V outlet. It overlaps the panel you seem to want to remove. Once the first panel is off, you can just grab hold of the left edge of the panel above the glove box and carefully pry it off.