Kneel on the kitchen floor in front of the dishwasher and extend the blade from a utility knife. Push the blade under the left side of the molding where it meets the floor and run it all the way to the right side of the molding to cut through the bottom of the caulk holding it in place.
Put on thick work gloves to protect yourself from burns and plug in the electrical cord of a heat gun. Open all windows and doors to help dissipate the heat and ventilate fumes from the melting caulk.
Set the heat level to medium and turn on the heat gun. Hold the air flow at least 3 to 4 inches from the molding. Hover the gun in place for 30 seconds, then slowly move it along the length of the molding. Turn off the heat gun and set it aside, using caution since the nozzle is hot after use.
Slide a putty knife blade or the flat end of a prybar under the base of the molding and pry it up from the floor. Once the end of the molding lifts, you can pull up the remainder, using your hands.