According to Mauser Pocket Pistols 1910-1946, by the late Roy G. Pender, your gun falls neatly into the "early postwar commercial" block. He documented serial #186703 given as shooting prize in 1919, and, since your s/n is higher, it is most likely going to be an early post WWI gun. Your gun has the heavy one line address on the slide, which ws later replaced around the end of the series by a two line address.
The "L.K." probably indicates police issue during the Weimar Republic period, especially since the mag is numbered to the gun which, as far as I know, was not done at the Mauser factory. (Someone else may chime on on what "L.K." means; I'm not up on German issue markings.)
Anyway, unless your great grandmother's brother served in WWII, it is unlikely that it was a bringback.
One note of caution about Mauser 1910 and 1914 pistols: Inserting the magazine is the correct way to allow the slide to go forward. Some users attempt to pull the slide back and release it rapidly without the mag inserted. This results in wear on the internals, making the pistol potentially dangerous. Also, be aware that when a fully loaded mag is inserted, it will automatically chamber the first round; Make sure the pistol is pointed in a safe direction when chambering a round as these designs become prone to ADs when worn.