It is an eagle over and H, a military proof used for a limited time in the late 1920's to early '30s.
This vintage luger is notorious for poorly struck acceptance and proof markings, yours are better than most.
Orders were given in 1937 to cease unit marking of police lugers; though not required some markings were "canceled", and example is below. Your markings may have been removed in the period, or at any time later; but are clearly police markings of a Schupo post.
You can see one below marked to the Landjaegeri (rural police) that was not touched.
Here is the same markings only tougher to make out! Both are 'u" suffix pistols.
Don't feel bad about "grasping" the details, it takes a while and not a little study. I like police lugers and have read all I could find about them and their first owners. Currently is have 35 DWM and Erfurt police lugers, along with a couple police marked M1896 Mausers and small "pocket" 7,65mm autos.
