The concept of refreshing a rifled barrel goes back to the days when muzzle loaders were state of the art. It is a technique of recutting the rifling of a worn barrel. In one form the rifling was actually recut, or deepened, with a cutter that used the remnants of the old rifling as the guide for the cutter. After the rifling was re-established the tops of the lands could be recut. When it was done you had a brand new rifled bore, somewhat larger than original. Being muzzle loaders, the difference in bore diameter could be made up with a thicker patch or a larger ball.
Rerifling was also common in the Schuetzen era, where a worn barrel was rebored and rifled to a larger diameter. It was not unusual for a .32-40 to become a .33-40. Because the rifles use either breech seated or muzzle loaded bullets, all that was required was a new bullet mold to fit the bore. While this may at times be referred to refreshing the bore it is really a rebore and rifle.
As to what the refreshing of the bore of the double rifle referred to is, one can only speculate. I suppose it could be either process. What is the rifle chambered for?
Glenn