I accidentally answered myself in the process of asking this question. This might amuse someone, so I'll go ahead and post it.
Question goes for both MAST and the HLA because it works in both. Why does the search for cat resolve to a gravitational lens, SDSSJ1038+4849 (Smiling lens)? One thing I do know is that a basic query at SIMBAD resolves, rather predictably, to the Cat's Eye Nebula (NGC 6543), so it seems to be something specific to STScI's archive service.
Some background on why I would even ask this: It was the first thing I ever tried searching for in the HLA, because I wanted to find something unusual for the ESA's Hidden Treasures contest a few years back. I do like cats. I thought I might discover on my own the reason for the search result over the years, but I now doubt I will ever know unless I ask. My first guess is that perhaps cat means something other than a fuzzy feline to someone, and my second guess is that someone else also saw the broad smile of the gravitational lens and was reminded of the famous Cheshire Cat.
Ok, I feel silly. I just answered myself by typing in full Cheshire Cat as a search and the same result appears. It would seem that the lens is indeed known as the Cheshire Cat to someone out there.