C API of the C implementation of OrderedDict was added in 3.5 together with the C implementation of OrderedDict. But it was never announced nor documented. Some macros contain bugs. PyODict_Check() and PyODict_CheckExact() are declared in the limited API, but don't work since use PyODict_Type not available in the limited API. PyODict_SIZE() is expanded to syntactically incorrect code and it's name is not consistent with similar macros: PyTuple_GET_SIZE, PyList_GET_SIZE and just added PyDict_GET_SIZE. Many names are just transparent wrappers around PyDict API (and they can't be different). Since PyODict C API is not documented, partially not working and partially redundant, and the C implementation of OrderedDict is optional (other Python implementations can provide just Python implementation of OrderedDict), I think this C API should be made private if not removed.
If the API is broken in the limited API then I definitely think we should consistently make it not part of the limited API. As for removing it I don't have an opinion without knowing how many people are using it.
With today's announcement of guaranteed ordering for regular dicts, OrderedDict just became much less important (almost insignificant). Also, the original reason for having this C API no longer applies. There is a reasonable case to be made for removing the API entirely (given that it was never documented, that it is buggy, and that it is no longer of any significance).
