Good news - A kind researcher answered the question in the Denmark Forum. "P. C. Nielsen" is Gena's father, Christian Holm. Since this is a Minnesota family, I'll post the new findings here.
Christian Holm was born Poul Christian Nielsen 02 Nov 1849 in Hørby sogn/parish, Dronninglund herred, Hjørring amt, Denmark. His parents were Niels Nielsen and Karen Poulsdatter. The family changed to Holm surname after immigrating to USA (emigration record March 1886 Copenhagen to New York on the Geiser lists them under Nielsen). Christian's brother Jens Peter Nielsen also changed his name to Holm and lived next door to Christian and Karen in the 1900 census Bath, Freeborn, Minnesota.
Poul Christian Nielsen married Karen Andersen 13 July 1876 at Hørby church (record found on Family Search).
They had two children born in Denmark, as found by researcher HRF (names and birth dates consistent with the family tradition):
1) Godfred Johansen Nielsen born 17 Aug 1876, parents Poul Christian Nielsen and Karen Marie Andersen (Hørby church book, image/opslag 36)
2) Jørgine Augustine O--? Nielsen born 21 January 1884, parents Poul Kristian Nielsen and Karen Marie Andersen (Hørby churchbook, image/opslag 46) <---"Gena Holm"
1880 Danish census Hjørring, Dronninglund, Hørby, Hørby Sogn, Hørbylundhuse er Hus, 9[F2], FT-1880, C2092 Poul Christian Nielsen 30 Gift Husfader Daglejer Hørby Sogn Hjørring Amt Karen Marie Andersen 27 Gift Husmoder Skæve Sogn Hjørring Amt Johan Godtfred Nielsen 3 Ugift Deres Barn Hørby Sogn Hjørring Amt Johanne Marie Poulsdatter 73 Enke Aftægtskone Astrup Sogn Hjørring Amt
Gena was born after that 1880 census but her brother Godtfred shows up.
1910 Eureka, Polk, Wisconsin Peter Jensen 26 born in Denmark Genia Jensen 26 born in Denmark Muller Jensen 5, son, born in Minnesota Nels Jensen 4, son, born in Minnesota Torvald Jensen 3, son, born in Minnesota Henry Jensen 2, son, born in Minnesota
Compare to birth records at the Minnesota Historical Society (mnhs.org):
Nels Christian Jensen born 09 Jul 1905 Freeborn County, Minnesota -- Mother maiden name: Nelson
Torval C. Jensen born 22 December 1906 Freeborn County, Minnesota -- Mother Maiden Name: Nelson
Henry Jensen born 06 Apr 1908 Freeborn County, Minnesota -- Mother Maiden Name: Nelson
On Family search, parents show up as Peter and Gena.