Pilot of a light airplane reported loss of directional control after landing and a runway excursion that resulted in minor damage.

Narrative

On Day 0 at XA30 while landing at ZZZ in Aircraft X; I experienced a runway excursion due to a wind gust that resulted in the aft; right lower wing trailing edge contacting the runway. Post flight inspection by an AP/IA determined the aircraft to be airworthy and just required cosmetic repairs.Event sequence: I received my landing clearance for XXR from tower and recall tower reported winds 120° at 6kts. At around 100 feet I put in my crossing wind correction. I touched down left wing low; right of center line. The left main and tail touched at the same time. The right main touched 1-2 seconds later and I began to decelerate straight down the runway. As I slowed through what I'm estimating 30-40 mph the left wing begin to rise at this point the stick was full left and aft; and with full right rudder . The plane begin to veer left I tapped the brakes twice trying to regain directional control then continued with continuous firm right brake pressure. At a speed of around 20 mph and heading 30 to 40° off the runway heading; the right aft wing tip contacted the runway associated with a tire squeal that could have been due to a skid or excessive brake pressure. I departed the left side of the runway into the grass. I did not make contact with any runway lighting that I'm aware of. I called the tower to advise I had departed the runway. Tower told me to hold my position. At this point I was in the grass at the edge of the runway; facing directly towards the tower. I could see the windsock off my left. Tower reported the winds at 120° at 6 kt but the sock looked like 10+ kts. After ensuring I was safe to taxi tower issued clearance to start and taxi to the ramp.