Unless the family was CERTAIN that the letter received was in Gertie's handwriting (and remember that because of the method to teach penmanship many people had a very similar penmanship style), you might try looking at newspapers in the counties between the area where she worked and lived. Foul play did occur in the 1920s, also, and unidentified bodies discovered at the time of her disappearance or later would have made the newspaper. The letter could have been a hoax from someone who knew the story and wanted to cash in. She may have given birth to a illegitimate or legitimate child during that time and that could be another area to explore. Other suggestions would be to see if she is listed in a city directory or state marriage index. Of course there is the 1920 census and the 1930 census will be released in a few years. Good luck.