There is also a rare Polish surname Zaik or Zajk which occurs about 1000 times in the
https://geneteka.genealodzy.pl/ databases (BMD).
No Stanisław in 1880-1890, though.
I also checked Zaich, of which there are also several hundred, including one, Stanisław Zaich, but b. 1887 and in Miechów (małopolskie), so no go.
I think "Grodna" could mean Grodno, which was in "Russian Poland" from 1795 until 1915, and is a large city. Unfortunately the above database only has very little data, if any, from territories now in Belarus.