“We need to do some greenfielding of this process”
This one is relatively easy to take apart, but you do need some prior knowledge of the green-field metaphor.
In the UK a greenfield is a fresh, new, undeveloped field; we even go as far to describe areas of greenfield land as green-belt and have specially designated areas for such. Green-belt development is normally regarded as a bad thing.
The opposite of greenfield is brownfield. This is land which has previously been developed and carries some legacy from that development. In the physical world a brownfield development might be an extension to an existing facility or the addition of a new facility within an existing development.
This concept has been taken on in a number of contexts giving us, for instance, greenfield software development projects. A greenfield project is fresh, new and undeveloped; starting without any consideration to what has gone before it and ignoring any of the constraints. Likewise software development projects that add to an existing capability are known as brownfield projects.
Greenfielding is, therefore, the process of starting afresh. I’m not sure why starting afresh isn’t used but that’s the mystery of most Office Speak. I think previously we would have used the phrase “we need to start from a blank piece of paper here.”
“We start each day with a blank sheet of paper in front of us, and what we write on it is up to us.”
John Larkin
Graham Chastney 
IMHO Greenfield is not “starting afresh” but never been done before, in most cases these simply don’t exist. “starting Afresh” is typical Brownfield stuff, You’ve bulldozed a site and are starting with something new, Buckshaw Village is a Brownfield site but starting afresh. The Only Greenfield scenario I can think of would be a case where someone starts a business with nothing but a vision and building for a scale they envision in the future, i..e Zero process, procedure, history
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Although, if you take that definition, nothing is greenfield – because, even the concept of “business” is brownfield.
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