WARNING: This page is about a different car, the 2011 BMW M3, 2010 BMW M3, 2009 BMW M3, and 2008 BMW M3. However, it is still accessible from the selected car via links, so may be relevant.
Release screws (1) and remove license plate light (2) from mounting.
Fig 1: Identifying License Plate Light With Screws
Courtesy of BMW OF NORTH AMERICA, INC.
Disconnect flat connector (1) in direction of arrow.