Hashimoto's thyroiditis is the most common cause of hypothyroidism in the United States;
Studies suggest a correlation between the stomach/intestinal bacteria, H. Pylori, and autoimmune thyroiditis/hypothyroidism:
Here is a study published May 2013 showing a correlation between H. Pylori and Hashimoto's thyroiditis:
The authors suggest that it may play a role in the onset of the disease.
In one study, addressing the bacteria improved thyroid lab tests, such as TSH, in patients who were not responding to high dose thyroid hormone therapy: