You say your grandmother entered the U.S. in 1922 as a minor? If you have her death certificate which statesher maiden name, that would be a start. Use that and start checking into the records from Ellis Island. In the meantime, while you are waiting to get that paperwork, ascertain the waiting time for immigrants before they applied for citizenship in the U.S. Canada had different waiting times before a person could apply for citizenship. During the '50's and '60's it was 5 years. Now it is 3 years. I forget what it was before that. But this will give a clue when you need to start searching to see if she did apply for naturalization and citizenship.
Also, check the 3 different postings that Harjeet had made in regards to the citizenship acts of Poland for 1921, 1951 and the 1960's. This should give you a start where to look. Also, ask any of the other relatives that you have in case they may have some papers from your grandmother. Did she have any siblings that might could still be alive? Are they in the States as well? Could they have any documents or letters from that time that could help?

 

As far as the entry date goes, again, check into the records from Ellis Island. Also, ask around in the family, especially the older members that may remember if your great grandparents said anything about giving up their Polish citizenship. That is why I mentioned about going through any photo albums and anything else that may contain letters or documents from the old country. Chances are, even with the 1920 act they still might have had to go through the nearest embassy to renounce their citizenship. Double check the citizenship act. If in doubt, get in touch with Lukasz Piotrowski. He deals with citizenship laws and qualifications. Since your great grandparents were born before Poland was recognized as a country in 1918, that part may cast some doubt. That is why you will need to start with the records from Ellis Island and with relatives. By trying to put together a paper trail on this side may help you to establish if you can claim citizenship. That is what I am trying to do as well. Any of your older relatives, if they kept documents relating to naturalization and citizenship should have kept everything in a central location.