Zinc-l-carnosine alone won't get rid of h. pylori though. But there have been several studies of it's use along with antibiotics for h. pylori eradication - some studies show it increases eradication rates, while others show it doesn't. Studies are on pubmed.gov. (Polaprezinc is the name of the compound in Asia).
What has not been mentioned is that all the studies on Polaprezinc are on animals, not humans. I did find one test tube study on human cells, but not in the body. In addition, the Polaprezinc is not being used alone, but instead is being used in conjunction with antibiotic therapy: