By what mechanism would light reflected from Earth be polarized? I would think that the light would be just as scattered as light emanating from the sun.
I don't think that they are looking at scattered light, which should indeed have isotropic polarization. I guess they are looking at directly reflected light. That light is reflected because the atmosphere of the planet has a higher refractive index than the vacuum in space.
If you take a look at the Fresnel formulas that are relevant in that case, you'll see that they depend on polarization if the incident light is not perpendicular to the surface. Especially interesting is the case when the light is shining on the surface at the Brewster angle: In that case the reflection of the polarization parallel to the plane of incidence drops to zero, while the polarization perpendicular to the plane of incidence is still partially reflected. So if you reflect unpolarized light at a surface with a real refractive index at the right angle, the reflected light will have perfect linear polarization.
For the atmosphere of planets you have to generalize these formulas to deal with a gradient change in refractive index, but the principle is the same. So if you collect light that has been reflected from an atmosphere on an angle that is not perpendicular to it, the light will be polarized. If you can measure the angle where the light is maximally polarized, you could then calculate the refractive index of the atmosphere. If you then do that for different colors, you might get some information about the density and composition of the atmosphere.
At least that is what I guess is the basic principle.