The filler panel is held on by a tab on top and two screws on the bottom.
Push downward on the top of the panel to free the tab. Hand pressure should suffice, the panel is quite flexible.
Once the tab is free, pull the top of the panel outward slightly so the tab clears the front fascia, then pull up gently to reveal the screws.
Use caution, if you pull too hard you can easily tear the plastic from around the screws, which may make it difficult to re-install should you desire to do so.
Color-matched license plate surrounds are available from West Coast Corvettes
http://www.westcoastcorvette.com and possibly others.