Gum disease causes excessive production of reactive oxidative species like superoxide, and hydrogen peroxide. 

These reactive molecules can circulate in the bloodstream and affect the liver and other organs.  Treatment of periodontal (gum) disease can reduce circulation reactive oxygen species in the blood.   

A whole body approach to dealing with reactive oxygen species with anti-oxidants may be helpful for gum disease, especially when you have other contributing conditions to periodontal (gum) disease, like a poor diet, smoking, and diabetes. 

more info here

https://www.sciencedirect.com/science/article/pii/S1882761608000860

Takaaki Tomofuji, Koichiro Irie, Toshihiro Sanbe, Tetsuji Azuma, Daisuke Ekuni, Naofumi Tamaki, Tatsuo Yamamoto, Manabu Morita,

Periodontitis and increase in circulating oxidative stress,

Japanese Dental Science Review,

Volume 45, Issue 1,

2009,

Pages 46-51,

ISSN 1882-7616,

https://doi.org/10.1016/j.jdsr.2008.12.002.