To prove that a forced transfer violates Title VII, must the employee prove she suffered "significant" harm? Or is "some" harm enough?

The US Supreme Court unanimously says "some" harm is enough. It need not be "significant," or "serious," or "substantial," or "any similar adjective." Muldrow v. City of St. Louis (US Supreme Court 04/17/2024): https://www.supremecourt.gov/opinions/23pdf/22-193_q86b.pdf

This is important because many lower courts have required an enhanced showing of harm.

Examples:

> An engineering technician is assigned to work at a new job site—specifically, a 14-by-22- foot wind tunnel.
> A shipping worker is required to take a position involving only nighttime work.
> A school principal is forced into a non-school-based administrative role supervising fewer employees.

The Supreme Court case involved a police officer who was moved from a plainclothes job in a prestigious specialized division giving her substantial responsibility over priority investigations and frequent opportunity to work with police commanders. She was moved to a uniformed job supervising one district’s patrol officers, in which she was less involved in high-visibility matters and primarily performed administrative work. Her schedule became less regular, often requiring her to work weekends; and she lost her take-home car.

As the Court put it, this changed the what, where, and when of her police work.

You can be sure this will result in an uptick in the number of Title VII cases that go to a jury.

Your results may vary. If you have this issue, consult a good employment lawyer.
(Not me, I'm an arbitrator.)