Look at the second image. See the orange square with the red border? It must be traversed twice. Also, see the black squares all connected? They act as train tracks. The orange square on it will travel to pick you up and will drop you off anywhere on the tracks.
I've done a lot topology puzzle apps. See the list below. Yes, I've done thousands of levels.
I like this game - particularly because of the train tracks. I solved all 75 levels of this game, but they took a while.
One thing I thought was a bit confusing at first: look at the last image. See the arrows that point down? They must be landed on from the tile above. Once you're on those squares you do not have to continue downward.
Some other good topology games:
Lines Numeric Fun
Colors the Addictive Game
Flow Draw A Line