The 1920 property stamp alone has little to no influence over value, but for those that are open to buying within this field (some are strict Imperialists or Kar.98k collectors) the presence of a property stamp can be a positive. I at least value a rifle that stayed in (official) German hands without interruption. What tends to depress Republican era rifles is less about the period (probably the most dynamic period in modern German history - dealing with adversity is often the best measure of a country, that it ended in the Hitlerites coming to power doesn't diminish what the Germans achieved 1919-1931, given the circumstances inflicted upon Germany a "Hitler" is hardly a surprising outcome, Oswald Villard predicted as much in 1914...) than the fact high quality rifles simply do not exist in number. The Kar.98b competes with Kar.98k prices, they have strong demand if found original-matching. Property marked rifles are almost always rifles that have seen several visits to a ordnance depot, often stretching into the late 1930's... (so many visits diminish a rifle imo) that is if they are German original at all... which the vast majority are mismatchers to one degree or another.
As for the property mark, it is covered in detail in the thread above. It has zero to do with the IAMCC or Versailles, or Spa for that matter. It was a purely German marking, no application to any inventory control measure. The IAMCC generally numbered a few hundred at any one time (in a country of over 60 million), mostly staff and typical flunkies that make up any military bureaucracy. Of these the meat and potatoes (basis, foundation, active core) amounted to a relative handful of inspectors (Officers mostly, typically technical fields, engineers) and researchers (pencil pusher and paper shufflers); these inspectors, mostly English, French and Belgian, but in the beginning American (until America refused to sign off on Versailles or the League... oh, the good ole days.. I do not believe any American's actually participated in inspections, I have read no reports, but they were involved in the forming of the organization), but also Italians, Japs. These Entente Officers worked with German military counterparts. Together they inspected German barracks, factories, forts, or whatever they wanted. Typically it would be a couple French and British Officers, German counterparts (Officers) and German support staff, often with German police escort, especially if in hostile areas (Bavaria, places where their activities were likely to cost Germans their jobs... which was common). Germans did the demilitarizing and destroying, all supervised by German Officers and certified by IAMCC Officers.
Needless to say they didn't count rifles or ammo, or compare ledgers to rifles, nothing was that idiotic or pointless. The IAMCC knew the Germans were grossly over limits, even before they left in 1927. The IAMCC focused upon the bottlenecks, - first the factories. Firms like Krupp had in-house IAMCC inspectors, they watched ammo factories, - without ammo a rifle is little more than a club, cannons rusty displays, the German Army (Heye's report upon relieving Seeckt) report to the German government in 1927 stated the Reichsheer had plenty of rifles (350,000), MG's (12,000), mortars and artillery, but only enough ammunition for one day of intense fighting. Really only enough for training purposes.
The other bottleneck the IAMCC focused upon was the effective's, they were constantly looking for hidden reserves of trained men, - they went after the German police and paramilitary forces religiously (the French were obsessed). The Germans were equally determined and made modest modifications and name changes, but never really altered their path. This happened under Ebert (socialist) and Hindenburg (conservative), the arrogance of Versailles and constant humiliations did more to unify Germans and Germany than anything else.
The property marking is a curiosity, the only thing it tells you is that it was in German government hands late 1920 through early 1921, nothing else, - that the Germans admitted at Spa that they officially possessed nearly a million rifles means that the vast majority of property marked rifles were subsequently destroyed 1921-1924.