Is it wrong to lock this stray cat out of my garage?

A couple of days ago I found a stray cat hanging out in my garage meowing at me. I fed it, and let it stay there while I was waiting for the humane society to open so I could have it scanned for a chip. I just went to have that done, and no chip. Since the cat was well fed, and looked healthy, they said its probably one of my neighbors, so just lock the garage door, and stop feeding it, and it will go back to where it came from. I felt like it was cruel, so I questioned them, but they assured me that it's the right thing to do. What do you think?

Is it wrong to lock this stray cat out of my garage?
Post Opinion