There's no set way to check that you removed all the trees until you beat the level, but here's the best way to find all the trees.
Start in one of the corners of the map (we'll say top left, for the guide). Slowly move your way right and check for any trees standing as you move across the row. When you hit the top right corner, move yourself down, and make sure that wherever the bottom of your screen was in the first place, is now the top of your screen (overlapping is obviously ok so you don't miss). Keep working your way back and forth, until you remove every tree, and then finish the level.
[Starting at the X, make this pattern back and forth]
X >>>>>>>> V
V <<<<<<<<<