From what I have seen and noticed on 88s I have, 88s refurbished in the 1920s had parts swapped (stocks, bands, magazines, bolts...etc) to make a functional and reliable firearm. I doubt the Turks would have cared if the rifle in question was an 88.05 or an 88.14 only that it worked and was reliable in the field. German parts that were swapped were not re-matched. The rear sights had the German graduations ground off and the re-applied in Fashi text.
Rifles refurbished during WW1 and the 1920s are typically in their original trim (receiver in the white, markings intact...etc) and are essentially in their "German trim" as they were given to the Turks.
For rifles refurbished during the 1930s, typically a re-blue of external parts was done. This included the butt plate, stock fixtures (recoil lug and rear sling swivel base, and lower barrel band spring), the receiver, the barrel jacket, and both bands. In addition, with the acceptance of arabic numeral system in Turkey in 1928, rear sights that were in Fashi text were ground off and arabic numerals applied. Typically, these rifles are mis-matched as they were rebuilt with available parts. Barrels may be the original one to the rifle or replaced .323" examples made by the Turks but retained in the Gewehr 88 trim.
For rifles that were completely rebuilt to closely resemble the 1903 pattern, a number of parts were retained and re-used to keep the cost down. Barrels would be replaced with newly made examples but it seems that 1903 style barrels were salvaged from older 1903 Mauser rifles and put on after evaluating two 88.05.38s I have. The stock can be a re-used 1903 Mauser stock that is hand inletted for the Gewehr 88 action and magazine or a newly made black circassian walnut piece. The give away between these two, besides the grain of wood, is the lower band spring of the 1903 stock versus the screw type of the Turkish made examples.
The 88 receiver is re-used with a hand guard adapter made to screw onto the barrel jacket threading. The barrel jacket post is cut off the barrel jacket and brazed onto the bottom of the hand guard adapter. A hole is drilled and tapped in the post to allow for the use of the 1890, 1893, or 1903 style cleaning rod. The upper band is a re-used 1890-1893, 1903 type whereas the lower one could be a re-used Gewehr 88 lower band or a 1893-1903 style band.
Bolt pieces are typically re-numbered with Arabic numerals to match the conversion.
Receivers were scrubbed of German markings on the exterior and the Turks applied their own property marking with the date and place of conversion.
As Claven has mentioned, some 88s may have German made bolt components though this is quite uncommon. One of my 88s has a complete German made bolt in her (an 88.05.38) though it is completely mis-matched. Two others have German made bolt bodies with their fire proof, acceptance, and serial numbers intact. Most that I have have czech made replacement bolts that are, I must add, very well made.
As for the crescent moon on the receiver, I do not know why some rifles received this and others did not.
The Turks used these rifles as front, and later, reserve arms up until the 1970s so I generally expect Turkish 88s to be mis-matched to some degree given German and Turkish part swapping.
I could post pictures of the three main types that I have identified to aid in the descriptions.
.
