H. pylori infection results in acute and/or latent gastritis which may impair folate and/or vitamin b12 absorption. MTHFR is responsible for the conversion of carbon-loaded folate into 5-MTHF (a folate with a single carbon group attached). This 5-MTHF is necessary for the conversion of homocysteine to methionine. If 5-MTHF is low, homocysteine can build up to toxic levels (especially to the brain). Potentially, with reduced folate absorption due to H. pylori infection, MTHFR could be less efficient. However, this effect would be quite minor. However, as we are currently studying in my lab, MTHFR genetic mutation is quite common and results in significant reductions in MTHFR efficiency. Therefore, the multiplicative effects of H. pylori infection and simultaneous MTHFR polymorphism could be significant. I realize this is an older question be feel free to contact me if you have further questions on this topic.