Closest I found > Klimki. 4 locations in Poland
Klimki 54°16' 21°42' E M U G Poland 142.2 miles NNE of Warszawa 52°15' 21°0'
Klimki 53°19' 21°30' E M U G Poland 76.6 miles NNE of Warszawa 52°15' 21°0'
Klimki 53°18' 23°15' E M U G Poland 118.7 miles NE of Warszawa 52°15' 21°0'
Klimki 51°58' 22°16' E M U G Poland 57.2 miles ESE of Warszawa 52°15' 21°0'
jewishgen.org/Communities/LocTown.asp
There is a Anna Parzych b. abt. 1888, who arrived Ellis Island in 1903. Her last residence is shown as Klimki
Klimki is the plural of Klimek, which is the diminutive form of the first name Klemens or (in the eastern borderlands) Kliment. It would be the equivalent of English Clem, the diminutive of Clement.
Those localities might be translated into English as Clems, Clemville or Clemton.
The Polish surname KLIMKA derives from the first name Klemens, coming from the Latin clemens (meaning quiet, peaceful, cool ...)