Garcinol, a compound found in both Garcinia cambogia and Garcinia indica, has been associated with anti-inflammatory properties. An in vitro study found that garcinol could decrease the expression of proinflammatory compounds such as cyclooxygenase-2 and TNF-alpha.[1] These findings were also supported by studies done on rats that showed Garcinia cambogia extract reduced other inflammatory markers like interleukin 1-beta and prostaglandin E2.[2][3]
However, there are no clinical trials in humans that show this effect, so more research is needed to show that this effect carries over into people with inflammatory conditions.