It is a "rubber road stamp", to quote postal terminology, see below.
The literature is not very helpful, but there are some short references. Specifically, the following Railway Mail publication:
Which mentions the "rubber road stamp" in the 4th scan as part of the description of the facing slip, which require the name of the clerk:
Facing slips showing round and straight-line versions of the rubber road stamp:
Also used by railway mail clerks on forms:
Also, the 1940 Postal Laws & Regulations volume noting backstamping requirements on registered and special delivery mail:
The examples I have handy are on "Special Delivery - Airmail" covers
Example 1, front and back:
Example 2, front and back:
Thus I would guess that the original poster's cover is also a "Special Delivery - Airmail" cover. It would be interesting to see full scans of the front and back.
I do not see any references on how to order one or whether the USPOD or the clerk paid for it.
The "Tr 39" is the Trip number.
Add: 2 straight line versions with the clerk name on a registry jacket from 1909: