Welcome to womanhood. This is going to happen when people see you as a woman. Women are at risk in situations where men might not be. That's unfortunate, we wish it were not true, but it is reality. Consequently, someone making that offer is being nice and a gentleman in certain respects.
Last year about this time exactly, before I'd legally changed my name but had been living nearly full time for several months, I visited friends in Memphis, Tennessee. I was stunned to learn that multiple men had asked a common friend (who they also knew) if I needed to be escorted back to my hotel, for my own safety's sake. At first it was surprise, then it was a welcome acknowledgement that people see me as the woman that I am, and that they were concerned for my safety as a woman.
Take it with a smile.