1920 Police Luger ??

[bruce4guns]

Gentlemen: I am just getting back into collecting and found what I consider a neat Luger. I have done as much as I can to identify it, but still have some questions so I am turning to this forum for help.
The gun is a 1920 dated DWM. The Date is in the proper position and does not seem to be a ground down over stamp. The gun is commercially proofed (Crown N) only. It has all matching serial numbers including the rear connecting pin ( Reichwehrminiceri mandate 1932 after production). The grips are not serial numbered but appear to be original to the gun or certainly period to the gun. The gun is fitted with the Schwi (sic) sear safety but does not have a mag safety.
The gun is accompanied by a holster serialized to the gun on the back (13) and with a Crown Anchor Proof. The holster was manufactured in 1918 by Hans Romer in Neu Ulm. It has been modified to Police standard by removal of the original buckle and the addition of the long leather strap with hole and eye. The holster has the following marks on the front S.Ar.I.II.13.
I assume this means Schutz Polizei Arnsberg First Centurion, Second Division or Squad and then gun 13 which is the last two digits of the serial number on the gun also. The gun comes with a pair of matching serial magazines marked 1 and 2 and a matching serialized take down tool. The gun itself has no unit markings on it .
My question is why where the unit marking x d out on the front of the holster? Is it possible that this unit was incorporated into the Army or the SS and the unit markings no longer were of meaning. This weapon is of considerable interest to me because it is an original rig that has stayed together with a 90% gun for 95 years and I am trying to learn as much as I can about it's history from the Wiemar Republic through the second World War.
Any further thoughts or input from this group or comments about the rarity or desirability (if any) good or bad would be appreciated.
Thanks for any input on this item.