Some research into WWI reminded me of those old songs. My mother, who was a very proper lady, had the same lyrics to Fritzie Boy but Mary Ann was slightly different.

Keep your shade down, Mary Ann,
Keep your shade down, Mary Ann,
Last night by the pale moonlight
I saw you, I saw you.
You were combing your auburn hair,
It was hanging upon a chair.
If you want to keep a secret from your future man,
Keep your shades down, Mary Ann.