Eligibility Check -- pre-1920s with return to Poland post-1920

Hi All! This is something I've been working on for a while. Six of my eight great-grandparents were born in Poland and I have two potential threads. I'll post this one first. I believe this to be a dead end but thought I'd check here.

What specifically I am unsure about is this: one set my great-grandparents came to the US in about 1905/1906 (obviously pre-1920s) but then returned to Poland post-1920. I understand family lore has absolutely no legal standing but I do wonder if it might suggest that there might be evidence in Poland of domicile and/or ways to determine if my GGF maintained his citizenship post-1920s. It was my understanding that he took the whole family back to Poland in either 1920 or 1921 to settle and live off passive income. But then they abruptly returned to the US in 1922. I assume because of the US Emergency Quota Act passed in 1921, i.e. they might have worried they could never return? Regardless, they did naturalize in 1930 (the initial documents were submitted in 1927).

On the ship manifests of his solo 1920 trip and the family's return in 1922 it lists him/them as Polish and I am not sure if that means they'd be traveling as recognized Polish citizens or would have documentation to this effect that would matter?

Thank you for taking the time to read this!

Great-Grandparents: 

* Date married: June 1907, USA

* Date divorced: N/A

GGM: 

* Date, place of birth: Jan 1885, Tarnów, Poland

* Ethnicity and religion: Polish, Roman Catholic

* Occupation: homemaker/tavern keeper

* Allegiance and dates of military service: N/A

* Date, destination for emigration: The first time she came to the US was in 1905; the second was in 1922

* Date naturalized: I assume same date as spouse, June 1930 (but I only have a photo of the card and only his name is listed but her name was on the Declaration of Intent)

* Date, place of death: May 1946, Chicago, Illinois, USA

GGF: 

* Date, place of birth: Oct 1880, Przeciszów, Poland

* Ethnicity and religion: Polish, Roman Catholic

* Occupation: saloon keeper

* Allegiance and dates of military service: unknown in Poland, none US

* Date, destination for emigration: The first time he came to the US was in about 1905; the second was August 1920 & third June 1922.

* Date naturalized: June 1930

* Date, place of death: July 1950

Grandparent: 

* Sex: Male

* Date, place of birth: July 1916, Chicago, IL, USA

* Date married: 1946

* Citizenship of spouse: US (her parents were also born in Poland but naturalized in 1933)

* Date divorced: N/A

* Occupation: butcher

* Allegiance and dates of military service: US Army WWII, enlisted 1941 or 1943 (records contradict) but discharged Nov 1945

(If applicable)

• Date, destination for emigration: he was born in the US but also returned to Poland with the family in the early 20s, returning in 1922 and is listed in those manifest documents as Polish
• Date naturalized: he is listed on his father’s naturalization intent paperwork from 1927
• Date, place of death: 1998, Chicago, IL, USA

Parent: 

* Sex: F

* Date, place of birth: April 1947, Chicago, IL, USA

* Date married: December 1971

* Date divorced: N/A

You: 

* Date, place of birth: December 1978, Chicago, IL, USA