Any granny who uses here cane-slinging ledge-climbing skills to save cats is a hero in my book.
That said, the ledge-climbing does stick a little. You may consider temporarily changing the collider's material friction property to zero while the spacebar is held down (if kinematic), or while granny's y velocity > 0 (if rigidbody).
Had good fun nevertheless. Good work, and good luck! :D