I have a similar faded (and cracked) badges problem with my Stilo's centre caps... but so far I didn't actually do anything about it.. but I want to get the wheels refurnished this year and the caps would show the wheels up, so they need a solution.
The badges seem to be plastic-welded into a hole in the centre of the caps.. though I'm reluctant to be sure... all the manufacturer would need to do is produce a flat faced cap and glue the badge into a recess.
But if you look on the back of the cap it looks like the badge has been bonded in place in an existing hole in teh cap... although this could be a red herring and it might just be a rough casting etc.
So.. this ^ has led me 2 possible solutions;
a) Drill out a hole in the centre caps that's 50mm etc. and fit regular, plug-in wheel centre caps, like a regular wheel without a centre cap has.
I'm expecting that the caps would have to be glued in place, since in a cap-less alloy wheel they are pressed into a recess whereas when fitted to a centre cap, they will only be held in by the thickness of the cap's plastic. They'd be loose for sure.
b) Lift off or otherwise un-bond the badge...chip it off etc. to leave a surface that can be made smooth enough to accept a stick-on gel badge.
I'm not sure what approach is going to be the best easiest, best looking or more durable but given the flexibility of the centre cap, I'd assume that a badge that is stuck to the surface of the cap will last better than one that fits "in" it.
Interested to hear other ideas for the best solution.
Ralf S.