Because the car has a clear coat, any fading of color in the color coat cannot be addressed as the clear coat will prevent you from reaching it and the the color difference you're seeing is at the basecoat level.
If there are
impressions in the clear coat from where the badges were you can probably improve and possibly remove these by using a product like ScratchX by hand or one of our cleaner/polishes by machine. The idea being and the goal to remove a little clear coat until you've leveled the surface in the affected area until it has a uniform appearance. Often time you cannot completely remove these impressions in the clear coat but you can improve them to the point to where you cannot see them easily with your eyes.
There's some related information in Meguiar's FAQ here,
5. Can a clear coat fade?
http://meguiars.com/faq/index.cfm?faqCat=Paint Questions&faqQuestionID=43§ion=_43#_43
Yes and No
The word fade means to:
"Lose color or brightness gradually."
Technically speaking, since the clear coat has no color, it cannot fade or lose it's brightness (at least if we use the above definition).
It can however become dull, but that's not the same as fading and is more typically a sign of oxidation and the build up of above surface contaminants. (See in this FAQ â Can a clear coat oxidize?)
Now lets ask the above question in just a little different way.
Can the color coat below the clear coat fade?
In short, the answer is yes, however, it depends upon the environment in which the car is exposed.
A car parked inside most of its life, far away from the equator will not show much sign of fading.
A car continually parked outside in a desert region close to the equator will fade more quickly and the results will be more apparent over time because of the increased exposure to UV rays.
While these answers are technically correct, the non-technical answer to the question, "Can a clear coat fade?", is yes, but very slowly. So slowly that most people cannot perceive any visual change over the course of normal day-to-day living or during the length of the ownership of their car.