While gum and other breath fresheners can attempt to mask the smell of alcohol, nothing can remove it. However, as the body processes the alcohol in the bloodstream, the scent should decrease until it is no longer noticeable.
Alcohol, unlike food, is not digested by the body. Instead, it is absorbed directly into the bloodstream from the mouth, throat and stomach. As the blood circulates around the air sacs in the lungs, the alcohol diffuses across the membrane into the air. The concentration of alcohol in the lungs, then, is proportional to the concentration in the blood. So, only when the blood alcohol content decreases should the smell of alcohol on the breath diminish.