They found that the forest planet peaks sharply in brightness when it is on the opposite side of the star as seen from Earth. We'd essentially be viewing the planet at its noontime lighting, and the tree canopy would reflect infrared and visible light into space (the proportions depending on the details of the alien world's photosynthetic processes). When the planet is on either side of the star, we'd be seeing the effect of long tree shadows cast by the early morning or late evening light.
The other planet models do not have the same unique rate of change in reflectivity during their orbits as the forest world does.
The models have to factor in the ever-changing influence of clouds on a planet's reflectively. This effect vastly complicates how the planet looks from day to day. In running their models, the researchers folded in a decade's worth of Earth observations from the International Satellite Cloud Climatology dataset (1986-1996). They found that what helps detangle the data is that trees backscatter light (like snowflakes illuminated by a camera flash), while clouds forward scatter light (like seeing fog in front of an oncoming car's headlights.)
This means that trees rise steeply in reflectivity as the planet approaches a noontime position, but clouds reflect much less.
Several weaknesses complicate the "exo-arboreal" search strategy. The team models a planet with no axial tilt, and in an edge-on orbit as seen from Earth. Therefore, the researchers do not take into account how astronomers could interpret the effect of seasonal variability. How does the planet look when the leaves fall off the trees in the autumn?
If the planet were tilted, the view should dramatically change as northern and southern poles are alternately tipped toward us during the orbit. This would complicate the planet's variability, especially if continents are distributed asymmetrically between the northern and southern hemispheres.
What's more, suppose the planet has a very exotic topology that mimics the shadow play of trees? For example, imagine if a significant fraction of the planet is covered with limestone pillars like Utah's Brice Canyon? Or perhaps the planet has a dried up seafloor that left behind tall limestone spires? Or maybe the world is covered in skyscrapers like the Star Wars megapolis planet Coruscant.