BCM - I have taken care of stray cats who were being fed/somewhat sheltered by more than just me. Also, if un-neutered or spayed - they will want to roam. Finally, my person and I had a stray who would come and hang out with us for a few days, disappear for a week or so, come back etc. We always got them neutered/ spayed/shots but otherwise let them be - feeding them and caring for them when they came around but not trying to otherwise contain them.
All of that was to say-the cat might come back on its own in a week or so.