Thanks to Jean and Rolland Campbell for sharing this old, used and abused, mystery plate with us. As you can see, it is plain white with the backstamp: Gift of American People Thru the American Red Cross.

It looks as if the organization has been using this phrase for many years, from at least 1917 through the 1970s.

In 1917, it was used with "The Khaki Song Book. For our soldiers and sailor boys." See abebooks.com.

Also in 1917, the "Knit Your Bit" program provided socks to military and civilians during World War I, and continued the program during WWII. See: redcrosschat.org.

In 1918, French-made cookies wrapped in brown paper were distributed with this phrase. See Google Books. And that same year, chocolate bars made by the Ideal Cocoa and Chocolate Company

During World War II, Coleman stoves were sent to Europe by the Red Cross with this same phrase.

We weren't able to find out anything else about the history of the plate, but it does seem reasonable that it was from the World War II era, and the Marshall Plan. As has been said, during WWI, most of the fighting took place in the trenches and not in the cities, so dishes wouldn't have been something that would have been needed in that war's aftermath to the same extent as after WWII.