Solution: Kara and the cloverleafs...

The main program leads Kara to the tree, calling the method invertLeaf before each step. This method tests whether Kara is on a leaf; if yes, Kara picks it up, if no, Kara puts one down.

def invertLeaf():
  if kara.onLeaf():
    kara.removeLeaf()
  else:
    kara.putLeaf()

invertLeaf()
while not kara.treeFront():
  kara.move()
  invertLeaf()