I'm sure you know what you are talking about, but when we visit schools individually as governors, it is not to inspect the teachers' work or to find fault, but to learn. We are not inspectors and, even if a governor happens to be an inspector, he or she has no jurisdiction over the teachers at that school but is just a governor on a par with others on the governing body. You should say to the teacher that you think you must have upset her, in which case you are sorry and hope that you can resume your previous pleasant relationship.
I'm sure she will respond. We have a responsibility to try to make our schools better, but only through decisions made together on the governing body and at policy level. Managing teachers is the head's job.