In a classic sense, the B737, doesn't have a real "Elephant Ear" like the DC-9 does, I believe they are mistaken. The elephant ear is more or less a fairing connected to the inner most portion of the inboard flap. This fairing (elephant ear), when flaps are retracted, fairs with the aircraft lower wing to body fairing, creating an aerodynamic fit with the flap and aircraft fairing.
This parts looks like a portion of the lower wing to body fairing. Elephant ears are classic back bruisers when flaps are down. Often a mechanic will hit his/her back on it doing inspections in that area looking for flap damage from the main tires.