"Open Source" has never been an OSI trademark, possibly because "open source" is a technical term for intelligence whose source is publicly available, such as books, newspapers, and magazines.  OSI's trademarks are "OSI", "Open Source Initiative", and the green logo.  "Open Source" was applied for by Software in the Public Interest as a certification mark signifying compliance with the OSD in 1998, but was abandoned the following year. 

The term is also an (irrelevant because non-conflicting) trademark for an Irish company for "research and consultancy services in the field of sustainable food and drink product development" and "whey protein for use as an emulsifier or binding agent in food", and for a New York company for "muzzle brakes that screw onto a rifle barrel".