Park the RV, turn it off and set the emergency brake. Flip the circuit for the refrigerator to off, for safety.
Pull off the grates from the fridge vents. Inspect the edges for cracks in the caulk or any missing pieces of caulk. These indicate areas where leaking is occurring.
Scrape off cracked or damaged caulk with the scraper and a utility knife. Wipe down the surface from the old caulk with a wet rag. Let the area dry.
Place the grates back onto the vents, and caulk around the edges of the grates -- making sure the caulk overlaps the grates' edges and the vents'.
Let the caulk cure overnight. Turn the power back on, and check that the caulk has fully sealed the leaks in the vents.