Be aware that after the man starts playing the cello with the squirrel's tail, the squirrel will throw a nut at him. This is part of the puzzle and requires a subsequent action.
The game presents several incorrect options for the cello string (vine, cat whiskers, necktie, curtain, electric wire); ignore these and focus on interacting with the environment. The key to solving the puzzle is interacting with the squirrel and finding the correct gift for the woman.