This may be Clara on the 1880 census. This is the only Gutermut (phonetical) entry that comes up in the entire 1880 census. However, her father was born in Germany and her mother Pennsylvania (not Ireland). Needs verification -

1880 US census

William MC CARTHY Self M Male W 49 IRE Farmer IRE IRE
Margret MC CARTHY Wife M Female W 43 PA Keeping House PA PA
Thomas MC CARTHY Son S Male W 19 OH At Home IRE PA
Mary MC CARTHY Dau S Female W 15 OH At Home IRE PA
Daniel MC CARTHY Son S Male W 14 OH At Home IRE PA
Tim MC CARTHY Son S Male W 12 MO At Home IRE PA
James MC CARTHY Son S Male W 10 MO At Home IRE PA
Frank MC CARTHY Son S Male W 8 MO IRE PA
Ellen MC CARTHY Dau S Female W 6 MO IRE PA
Maggie MC CARTHY Dau S Female W 4 MO IRE PA
Charley MC CARTHY Son S Male W 7M MO IRE PA
Clara GUTERMUT Other S Female W 18 PA Servant IRE IRE


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Source Information:
Census Place Jackson, Livingston, Missouri
Family History Library Film 1254700
NA Film Number T9-0700
Page Number 41B