Previously, if your project used one of the main OS licences you were good as far as they were concerned. They mainly existed to avoid lawyers coming up with licenses that water down the rights an open source license provides.
own the trademark of “Open Source”.
They tried, and the USPTO denied their application for same. As such they have any such right to exercise.
They own a trademark for “Open Source Initiative”, and attempt to persuade the public that they alone define the term “Open Source”.
Nevertheless, their Open Source Definition is reasonably respected
> the use of the term “Open Source” is used solely in reference to software distributed under OSI Approved Licenses. [1]
So you can refer to any software as "Open Source," regardless of their definition. But, if you call a piece of software "Open Source" alongside the use of the Open Source Initiative's trademark, then you must also use their definition of "Open Source," unless you otherwise have written permission.
So every time I talk about open source I'm a dirty trademark infringer and IP pirate?
The fact that they have fooled so many people into thinking they own a trademark on a generic phrase is, however, pretty impressive.
In the US you can trademark and patent H2O if you insist a bit, so it wouldn't surprise me if they actually owned the actual trademark.