Little Critter Hansel and Gretel: a lift-the-flap book by Mercer Mayer, 2010.
Not surprisingly, this book has the most radical changes to the story that I've yet seen. Of their own volition, Hansel and Gretel happen to be taking a walk in the woods, when they are warned by a black bird to turn back. They ignore him and go to the witch's sweetie house, but instead of eating it, they ring her doorbell. She feeds them enchanted food and later puts Hansel into the dungeon with the usual plans to fatten him up. Gretel tricks her into helping retrieve a bucket from the well, and pushes her in. The evil witch emerges grumpy and dripping, but here comes the children's father, who has been searching for them all along. They go home, leaving the witch stuck in her well. There is no verse used and the bird provides brief running commentary on the action.
This book uses the heavier cardboard pages appropriate to a lift-the-flap title. Hansel and Gretel are cute, bucktoothed furry creatures readers will recognize from any of the Little Critter series books. The red-eyed hag in the woods appears to be an alligator or a dragon in a typical black witch's outfit, including peaked hat. Kids can lift the flaps to find things like the witch's candy house, Hansel sleeping in a sack, a mouse and a crumb in an otherwise empty breadbox and more.