RV10 pilot reported failure to disconnect tow bar resulted in loss of aircraft control on landing; prop strike; and runway excursion.

Narrative

On the morning of Day 0 at about XX:00 I pulled the aircraft from the hangar to the tarmac using the tow-bar for a flight to ZZZ. The tow-bar is difficult to remove single handedly; so I waited for my partner to help and in the meantime; I did the usual pre-flight check. My mistake was forgetting to remove the tow-bar and to do a final walk-around just before entering the aircraft. We taxied onto the grass runway and departed with no issues. When landing at ZZZ on Runway XX; we landed normally. The aircraft touched down at about 60-65 knots. As the aircraft slowed to roughly 25 knots there was a slight shimmy; and the aircraft began to veer right. I pressed left rudder and then left braking. The aircraft maintained its direction (about 10 degrees off to the right). I applied both brakes gently and then more firmly without skidding. As the aircraft slowed it seemed to turn at a tighter radius. I advised passengers of the oncoming off runway incursion; but it would be okay. At about 5 mph the aircraft turned more to the right and exited the right side of the runway at almost 90 degrees and I applied full up elevator and relaxed the brakes to lessen the downforce on the nose wheel onto the grass. There was no side load or pressure. There was a slight thump and the aircraft gently stopped about 10 to 20 feet onto the grass. The engine was running; and all systems seemed to operate normally. I called ZZZ traffic to advise of my position which was about 2000 feet down the approach end of Runway XX. I then powered off the electronics and shut the engine down. I became aware of the propeller damage after shutdown as there was no vibration while running. Upon exiting the aircraft; I learned of the propeller striking the nosewheel wheel pant as it had turned beyond its travel. The nosewheel was inflated. The tow-bar was resting near the nosewheel but unattached and undamaged. I advised airport personnel of my incident and position once at the FBO and they used the airport golf-cart to tow the aircraft to the ramp. I provided information to the airport personnel as requested. I will be taking a well-deserved lesson learned takeaway from this incident and firmly committing to a final walk around just before entering the aircraft; as a minimum.