Might have gotten luckyfor Anna's maiden name- there is a family tree on ancestry.com that shows Anton and Anna
They show Anton born March 12, 1889 Minsk, Belarus, died Aug. 27, 1959 Bridgeport, CT
wife Anna Zinko born August 4, 1891 - no death shown for her
they don't show a source for her maiden name - in 1930 she is born about 1895 but census are not always right so I suppose their birth date for her may be right - too bad they don't give a source for any of their info.
The birth date for Anton is not what is shown in the WW11 draft - Feb. 15, 1891 but the death date is right.
CT death record does not show her birth date but she died Jan. 9, 1958
If you sent for the death records for Anna and Anton they may show her maiden name and maybe even names of parents.
I looked for Anna Zunik coming to US and there is one who may be right of your Anna.
New York Passenger Lists, 1820-1957 about Anna Zunik Name: Anna Zunik Arrival Date: 16 Jul 1913 Birth Year: abt 1894 Birth Location: Austria Birth Location Other: zalanow Age: 19 Gender: Female Ethnicity/Race/Nationality: Ruthenian (Russniak) (Ruthenian) Port of Departure: Hamburg Port of Arrival: New York, New York Ship Name: President Lincoln
Her passage was paid by her brother and she is going to her brother Andrus Zunik of Newark, New Jersey - I cannot read the name of her contact in Russia
There is an Andrew Zunik living in Waterbury, CT at time of World War 1 draft He was born April 3, 1881 Russia
I don't see him in 1920 census though so not much help there.