She is afraid that the mere mention of the word "gun" will ruin her teaching future.
Why would she have any need to mention it? No need to tell anyone at all that she or you has a CHL. If you were an open carry activist, I could see the need to be concerned, but she really needn't worry so much.
I work with the public and lots of kids in my job. I also talk guns with some patrons "in the know" about my guilty little weekend pleasures
As it's a small town, I know the residents all talk to each other. But if you are not creepy and do not carry yourself as a future serial killer, no one is likely to be overly concerned.