Don, it sounds like a Stoeger American Eagle exported to the US during the 1920's. I would imagine the "inspectors mark" you mention under the serial number is a lower case "t". It is part of the serial number. We refer to it as the suffix.
I assume that the serial number is either 7810t or 7801t. If so you should find the number 01/10 on the underside of the take-down lever as well as in several other places on the pistol.
You state that the safety area is marked "GESICHERT". I find this odd as I would expect all Stoegers to be marked "SAFE". How is the extractor marked, "GELADEN" or "LOADED"? Before judging its value, we would need to see photos.
The "GERMANY" stamping under the serial number, is it marked through the bluing or under the bluing? Is there a second such stamping on the right side of the frame near the Stoeger markings?
" 'To everything there is a season...a time for war and a time for peace'. and this is the time for war". Reverend Peter Muhlenberg, January 21, 1776, Woodstock, Virginia