BUZZ! Not quite right.

In fact, there's a Law of Conservation of Momentum, so the Earth can't lose momentum (without transferring it elsewhere, but there's no elsewhere in this scenario).

(Nor is the momentum mainly caused by water, but by the mass of the Earth itself, but that's irrelevant.)

In fact, the reason the Earth slowed down a little was because of the Law of Conservation of Momentum!

Momentum is mass times velocity. But the further a mass is from the center of the Earth, the faster it rotates - exactly like a record, where the center point is motionless and the edges move fast.

So if you raised 39 trillion liters of water by 175 meters and the rotation of the Earth stayed the same, the Earth's total momentum would increase. Because of the Law of Conservation of (Angular) Momentum, that cannot happen - so the Earth slows down a tiny bit.

You can see it in action in this professor's demo: