The US Army Transport Service (USAT) operated ships to move troops and cargo between the United States and overseas ports. In 1942, the Transportation Service became the Transportation Corps.
https://en.wikipedia.org/wiki/Transportation_CorpsThis letter was mailed on the vessel "Republic" and was "posted on the high seas" meaning it was mailed on the ship somewhere in the middle of the ocean between ports. It eventually (4 days later) entered the USPOD mail stream in San Francisco.
In 1935, Republic was servicing the New York—Panama—San Francisco—Honolulu route.
https://www.navsource.org/archives/09/22/22033.htmOne purpose of the Army Transport Service datestamp is to know when the person actually posted the letter, perhaps if a payment needed to get in the mail by the 1st of the month, for example.