Dear Ms. Kaminski,
Thank you for posting your request on History Hub!
Generally, the number in the "Travel Document No." column would refer to the document each traveler provided to show their eligibility to enter the U.S. In most cases that was a visa or return permit. The Reentry Permit was introduced shortly after the Immigration Act of 1924, which prohibited the admission of any immigrant without a visa or other travel document. Since returning immigrant residents could not get visas, the Immigration & Naturalization Service (INS) created reentry permits beginning around 1929. Most of the reentry permits from before 1944 no longer exist. The Reentry Permit Files from 1929-1944 were scheduled as temporary records and destroyed by INS. The USCIS History Library still may maintain a card index to the early permits, but the files no longer exist. Any reentry permits from 1929-1944 that exist today were later consolidated into Alien Files (A-Files) or Certificate Files (C-Files).
A-Files were created in April 1944 as a point of consolidation to include all of the records of an immigrant. It is possible to locate reentry permit records dated after this point (and both reentry permits and A-Files are records that are still created by USCIS today). Depending on the individual's year of birth, an A-File may be found at either NARA or USCIS. NARA has some of the A-Files for individuals born 1918 and prior [see the series Alien Case Files in the Records of U.S. Citizenship and Immigration Services (Record Group 566) that are searchable by name using the National Archives Catalog]. USCIS maintains all A-Files that have not yet been transferred to NARA for permanent retention. Researchers may request records using USCIS Genealogy for early A-Files and all C-Files OR USCIS FOIA for more recent A-Files.
If you should contact NARA, due to the COVID-19 pandemic and pursuant to guidance received from the Office of Management and Budget (OMB), NARA has adjusted its normal operations to balance the need of completing its mission-critical work while also adhering to the recommended social distancing for the safety of NARA staff. As a result of this re-prioritization of activities, you may experience a delay in receiving an initial acknowledgement as well as a substantive response to your reference request from NARA reference units. We apologize for this inconvenience and appreciate your understanding and patience.
We hope this information is helpful. Best of luck with your research!