AFTER FURTHER REVIEW...
"Dear Honey,
Shitty is a boy. Neutered of course, or I would’ve noticed sooner. Now I don’t feel so bad about the name. Also I saw the cat that belongs to the lady behind us, similar looking but with a very bushy tail, and I don’t think she lets it out much, if at all. I saw it sitting inside the glass door. So I don’t know if Shit Rat has a home or not."

I told him that makes us look really stupid for not figuring it out sooner, but in our defense, he/she never let us spend much time poking around in the under regions, and there wasn't a big need to know.
About the name, it is taken from the Canadian TV series "Trailer Park Boys." The trailer park manager hated cats and called them shit rats. Mr. Troutbend started calling this cat that name because it used to come look in the patio door and hiss at us. That was before it decided it liked us; now we're all pals. I soften it a little by spelling it Chitty.