It was called chayote, a native of Mexico that spread elsewhere in time. In the Sunset article, a lady in Los Angeles was growing them in her backyard, and a photo of the vegetable was included.
Underwood wrote to the lady, asking if she'd mail him chayote seeds in exchange for seeds from Guam plants. She said yes. This episode was written up in the Guam Recorder in 1936.
Once the seeds got to Underwood, I assume he grew them or gave them to someone to grow and from there it spread among the people.
Since it includes a sensitive word, I will not spell it out completely. The lady in the video says it, so you'll know it from her.
Many Chamorros in those days found it easier to pronounce Underwood as Andaut. That is, AN - DA - UT (OOT).