A reblue is a re-polish of the metal surfaces, and then reapplication of the chemicals that turn the steel blue in order to reduce the tendency to rust.
If you look at the uneven lines on the sideplate of your Luger and compare them to other photos of the Luger sideplate, you can see that the sideplate on your Luger has been aggressively polished and "blurred" the straight lines made by machining... so much so that the last two digits of the serial number that should be on the exterior of the sideplate are almost invisible...
The other surfaces in your photos are too shiney to have been the original military finish for a P.08 made by Mauser... so this gun had to have been refinished. Perhaps it happened before you were old enough to even know the pistol existed in your household, but it did happen none-the-less.
Compare your photo of the left side with this other byf 41 Luger and see the crisp lines on the sideplate... this gun has the typical military type finish of the time... Yours has changed since being manufactured and issued to the German military.
