Use a plastic pry tool to dislodge the badge from each specific insert point going all around alternating insert points. Once the badge feels loose all the way around (dislodged at every point but still attached), pull as straight out as possible all at the same time. Pull as leveled straight...
When you first turn on the vehicle ... is your A/C on? ... sometimes that extra (immediate) load requirement makes the electric power train require instant ICE power and it may create noise and rattles in the snap transition.
Try using a few wraps of "Teflon" (a.k.a. "Plumbers") tape ans see if if helps ... might be item specific or ball connection specific, mine doesn't rattle ... I also sprayed painted mine black.
Never use an unattended battery charger in an improperly ventilated area and one that does not have (multiple) in line fuses as (multiple) protection ... some items/devices require basic knowledge of the thermodynamics and electronics of the device and require some common sense on the part of...
All of the above + ... is the A/C on when you start your vehicle? ... if so, it is likely to switch the ICE on straight away to handle the extra start up load and keep it going for a while ... the engine may shudder for a moment at start up when it tries to run on electric but the computer says...