I found a Petro Wytik from Austria, but nothing from Poland.
First Name: Petro
Last Name: Wytik
Ethnicity: Austria, Ruthenian
Last Place of Residence: Wroblik, Austria
Date of Arrival: Aug 02, 1909
Age at Arrival: 40y Gender: M Marital Status: M
Ship of Travel: Martha Washington
Port of Departure: Trieste
Manifest Line Number: 0029
This may be a little too old to be your grandfather's father, since this guy came to the US at 40 in 1909. But Whityck does not look Polish.
I'll keep my eyes open for anything though....good luck.
I found it on the Ellis Isle website. It's a free site, so you can type in Wytick, Whitick, Whytick, Widdyk any another way of spelling it.
I typed in Petro because Peter just isn't something a Polish mother would have named her child in her Native country back in those days. LOL I used to have roadblocks in my family tree too (French-Canadian) because the first paid Genealogist erroneously wrote all names in English...Peter instead of Pierre, and John Baptist in stead of Jean-Baptiste, etc.