First, about H. pylori the literature states: Infection of the stomach with H. pylori is not the cause of illness itself; over half of the global population is infected but most are asymptomatic...
The upstart of this is - some natural control of the invasive gastric pathogen is good practice. lj has outlined some natural remedies to bear in mind. For example, a regular regimen of probiotics makes sense. It is known, but not universally practiced in the medical profession, that disease that requires heavy doses of antibiotics - such as sepsis or cellulitis - can wipe out normal intestinal bacteria needed for digestion and absorption of nourishment; the result is diarrhea or irregular stools BUT more importantly, it often gives rise to clostridioides difficile - C diff - and that can turn problematic or even fatal.
Many hospitals and medical practices urge patients on antibiotic therapy to maintain a daily regimen of regular OTC probiotics - to fight the C diff and maintain reasonable bowel functioning. Many do not urge supplementation. In my city such supplements are encouraged with antibiotic therapy but 70 miles west of here they actually discourage supplementation. A dear FReeper friend of mine was lost at least partly to C diff due to this oversight.
Also a non bacterial (plant, or 'floral' based) probiotic is a valid consideration since antibiotics don't affect plant based supplements. The best known probiotic of this type that is available in most drug stores is called Florastor; it may be cheaper in a vitamin shop as Saccharomyces boulardi (sp?).
The lesson here is that one way to fight digestive bacterial infection is to maintain a daily regimen of regular probiotics.
However, H. pylori is a pathogen prone to mutations and some mutant strains are considered virulent and potentially dangerous. So, while I agree to regular natural controls with probiotics and dietary supplements, I would caution that virulent resistant mutant strains of H. pylori that survive the probiotic should be treated with an antibiotic, specifically Flagyl (metronidazole.) While on the antibiotic continue with regular daily probiotic dosing, even increase it for the time.
One interesting side effect of the Flagyl for me when I took it was that a 25 year misery of rosacea, which was getting worse by the year, was wonderfully cleared up and has not returned for well over a decade. 😎 I have tried to get the info out to the medical profession that, instead of treating rosacea with ongoing antibiotic therapies - to which the body builds up resistance as well as various pathogens - try a standard gastric dosing of metronidazole for 10 days to two weeks. I do believe the idea is catching hold!
Thanks for that info. I had rosacea for maybe... 2 or 3 years and it was painful and disguring. I got rid of it by a very unusual method.