Ancestry.com has a database titled BORDER CROSSINGS:  FROM MEXICO TO U.S., 1895-1964 There are  1,338  people listing Greece as their place of birth.   Remember, if you don't have a subscription to Ancestry.com you can access if for FREE at most public libraries. Note:  FamilySearch.org also has a database on Border Crossings:  From Mexico to U.S., but it only includes the years 1903-1957 DATABASE DESCRIPTION This database contains an index of aliens and some citizens crossing into the U.S. from Mexico via various ports of entry along the U.S.-Mexican border between 1895 and 1964. Specifically, this database covers the following ports, years, and records: Arizona Ajo, Lukeville, and Sonoyta, Arizona (Jan. 1919-Dec. 1952) and Los Ebanos, Texas (Dec. 6, 1950-May 26, 1955) Index to Manifests of Aliens Admitted for Permanent Residence, Jan. 1, 1919–June 30, 1924 Manifests of Aliens Admitted for Permanent Residence, Jan. 1, 1919–Jun...