Stealing a Cat?

So maybe about a month ago we took in a stray cat. She really is a sweet kitty and was just always hanging around our apartment wanting in. One night when I came home from work on a cold rainy evening she was huddled on our doormat crying. I of course could not leave her outside and I let her in. Nate bought her food and the poor thing seemed starving! We call her kitty and we love her. She's kind of our part time cat. She comes and goes and sleeps over myabe once or twice a week. Doesn't tie us down but she's kind of fun:) Today we found out that Kitty is not the stray that we thought she was. As we were leaving this morning to go watch conference , Kitty followed us outside and down near our car. As we were coming down the stairs a woman on her porch saw Kitty and said "Shadow where have you been?!" Nate I walked a little bit quicker to the car and hid our laughter since she had been staying at our house the night before.....Hmmm don't know what to do now....