It's hard to know. I took it as a joke, that the human version of Jeffries is the unofficial version and his current version is now the official version. But no doubt there are other ways to explain it.

I wondered this too....(have another thread inquiring).

I took it to mean that Cole will have a memory of how we remember the events of Twin Peaks...those being the "unofficial version"....and that he will not have memory or know if Cooper succeeded with his mission (going back in time to save Laura & "changing dimensions" becoming Richard....this being the Official version.

Not sure how that all plays out or fits together.

would seem that if is there part of this Blue Rose case we don't know about (and shared within the task force), I would think that the Unofficial version would be wiped and Cole would only know the Official version....my theory seems to fall apart quickly, but i still like it vs it being a "joke" about the old vs new Jeffries.

a tea pot who was a man before and disappeared long ago tells you to say hello to some old friend, adding that he will remember the unofficial version. this context strongly suggests that the unofficial version is his human form.

i wouldn't go for another answer because gordon and philip jeffries didn't have any chance to communicate after the disappearance. gordon can't even remember exactly the content of their last encounter. Gordon clearly states that, jeffries told he was after Judy and he disappeared. That seems the end of their communication.