These people are not in Bareily, but in the outskirts of Bariely (see the last episode of IB before DBO), so I assume that this is a village which is slowly getting into the jurisdiction of Bareily Municipality (happens whenever a city expands, the nearing villages become a part of it)
About Gauri studying in a good school, I doubt, as a class 5 student who is from an English medium school can tell the difference between "Sh" and "S", her vocal is actually a blunder (sometimes like a person who is ganwaar and sometimes like a person with good knowledge) probably since writers are themselves not sure about it
Anyhow coming to your topic, yes village girls are not ganwaar and without self respect, but then they are raised with a mindset that marriage is a divine thing, (forget about village, even in the metros girls are taught that marriage is a one time thing and try to protect your marriage even if it means you accepting a few false acquisitions ) and that is what the mindset of Gauri is, for her a man protecting her life and putting sindoor wasn't a small thing
And then why wouldn't she want to save a marriage which she feels is true and has been done with a person who she is knows is a good person who can protect him from the world and who is angry just because of a misconception, to be frank, he isn't even angry at Gauri, he is angry at the girl who he thinks Gauri is