It looks like some sort of reaction to a cleaning washing product that’s been used. Do you wash your car yourself or entrust it to one of the many £xx’s hand wash type places? If the latter, be aware they often use very harsh cleaning products to remove dirt quickly, as that means greater throughput of customer cars which means more income for them. If you wash your car yourself, then check the cleaning products you use to ensure they’re ph neutral.
You could try a polishing compound to see if that’ll remove the marks. If it is a reaction between the
badge material and a cleaning product that can’t be rectified by gentle polishing, the a replacement
badge would be the solution.
If you do need a new
badge and fit it yourself, be sure to measure the position of the existing
badge before removing it so the new
badge can be attached in the same place.