Will carbamide peroxide reduce tooth enamel?

No, it should not: Carbamide peroxide is a commonly used whiteing agent that esentially is the same as hydrogen peroxide but about 1/3 potent.

Very slightly: Carbamide peroxide is a very common ingredient in many dental professional teeth lightening products and toothpaste. Professionally applications of carbamide peroxide have been shown to have very little associated damage to enamel. Recently, there was a clinical study that showed some demineralization of the enamel, but only at the "nano" level-- only significant if it were overused.