I am not so sure about the maker being Gustav Klingert. He very seldom used Latin letters i.e GK in his punches. Usually he punched ГК., КЛИНГАРТ, KLINGERT rarely GK. Note with a dot! (if he at all used GK, it is as for now still a bit unclear.) Undoubtedly the letters looks very much like GK (Latin) but more like Cyrillic CK (Latin SK). That would be Semen Kasakov in St Petersburg around 1889-1900 also known for his enameled objects, P#2881. Use the search function with "Kasakov" and you will find more information and discussions about the mark, him and Klingert. In addition, the photo of the set is not clear enough to see the enameled pattern. It would probably have helped to see it.
About the "strange" hallmark. Goldstein already mentioned that it is a Latvian remarking punch used after Latvia became independent 1918 (-1945). Without this mark silver objects could not be officially sold in Latvia.