A thought …
Pronouniation of these two names is very different. In Guittre the g is a “hard g” as in the English “go.” In Gittre, it is a “soft g”, think of the name “Georges” which sounds like it might begin with “zh.” So, I think these would have been, or should have been, written differently by an English speaker.
However, with the orthographic creativity of the census takers, anything is possible!
I concur with Day.