I've just noticed this in the maintenance menu. It's at 67% which is the same as my paintjob. Is it just the paint?
It isn't the paint, but integrity and paint both wear at the same rate: they both lose 1% for every 100,000 Ls travelled in Supercruise. The dev post linked above mentions other things which are supposed to cause integrity loss (like repeated high-G maneuvering) but the only thing we've ever noticed to cause a loss is Supercruise travel.
So it's possible to honk'n'scoop your way to Sag A* and back, and still have 97% integrity left. But fly to Hutton Orbital (6.2 million Ls away from the jump-in point) and you'll lose 62% of your integrity. It's worth bearing in mind if you're tempted to fly to Hutton a couple of times, just to get your paint to 0%. Repairing paint is cheap, repairing integrity is expensive, especially for the costlier ships.