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.

void invertLeaf() {
  if (kara.onLeaf()) {
    kara.removeLeaf();
  }
  else {
    kara.putLeaf();
  }
}

public void myProgram() {
  invertLeaf();
  while (!kara.treeFront()) {
    kara.move();
    invertLeaf();
  }
}