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).
If you have h. pylori, don't take iron! You're feeding the biofilm. You're probably iron deficient because of the h. pylori - it binds iron, transferrin and lactoferrin, it uses the minerals (iron, calcium, magnesium) to build biofilm which makes it more difficult to eradicate. Avoiding iron until you get rid of the h. pylori is a good idea.