Adding onto the deleted dialog, McCoy may have indirectly pinpointed the era of the colonization of the planet, Omega Four:
MCCOY: Our tissues definitely show a massive infection, Jim, but something is immunising us down here, thank heavens, or we'd have been dead hours ago.
KIRK: I don't think we're going to have time to isolate it, Bones.
MCCOY: The problem is, it could be anything Some spores or pollen in the air, some chemical. Just finding it could take months, maybe even years. And I've only got one lead. The infection resembles one developed by Earth during their bacteriological warfare experiments in the 1990s. Hard to believe we were once foolish enough to play around with that.
The planet was colonized after the 1990's, perhaps an early space race between the U.S. and China where both put a colony on the same planet. Isolated from Earth forever, and years later, politics get out hand and a biological warfare breaks out between the two colonies. We could be taking about a limited population over a smaller area on the planet.
The timeline is off, though:
TRACEY: Their year of the red bird comes once every eleven years, which he's seen forty two times. Multiply it. Wu is four hundred and sixty two years old. His father is well over a thousand. Interested, Jim?
KIRK: McCoy could verify all that.
TRACEY: He will if you order it. We must have a doctor researching this. Are you grasping all it means? This immunising agent here, once we've found it, is a fountain of youth. Virtual immortality, or as much as any man will ever want.
Tracey thinks that Wu's father is over a thousand years old, which can't be true if Earth's early space colonization period was only 200-300 years ago and the Constitution was written in 1787 which would be about 500 years ago. To counter the time issue, Kirk is not convinced about their extreme ages, saying McCoy would need verify it, and even Tracey wants McCoy to verify it either implying that he wants to proven right, or even he is open to the medical truth and wants proof one way or the other, but regardless of the results, Tracey is still convinced that the inhabitants are very old.
Deleting the Earth dialog eliminates the time discrepancy and puts the mystery of a parallel world up to our imaginations.