I doubt you would find any studies linking reuteri to parasite killing. The best you could correlate would be that it probably has bacteria and yeast killing properties. It is a remote possibility that it might have some action to a nematode parasite.
Take care of your teeth and gums, this is a hiding place for many bacteria. These bacteria produce toxins that circulate in the body causing inflammation. With inflammation you get degenerative diseases. It causes cellular damage (oxidative stress), taxes the endocrine and immune responses.
Brush thoroughly which mechanically removes biofilm (plaque), use a natural mouthwash that has essential oils which kill off the bad bacteria. I alternate with hydrogen peroxide. Also floss, which reduces the bad bacteria. Studies have shown that regular flossers have increased life spans which is correlated with the inflammatory processes. Your immune system will thank you.