I guess I don't know what to do when someone I don't know waves and smiles at me...

I was doing leg lunges at the gym and a girl, a woman I guess, waved to me and smiled as though she knew me. I looked around to see if she was directing her attention at someone else, but there was no one in front, in back, or to my sides. So, I didn't know what to do because I didn't recognize her; I didn't know who she was. I still don't know who she is.

I politely smiled back and she paused and then continued with her workout. I assume she thought I was someone else. I'm not sure if I should have done something more or else. I wonder... Later, I saw her walk out of the gym.