I just checked mine, and it's on there quite firmly. This guide to installing a new aftermarket shift boot onto the stock plastic piece you're talking about has pictures of the back of that plastic shifter trim piece and shows the clips-
https://www.redlinegoods.com/Fiesta11install.php#ST
It does appear that you should be able to snap that piece off and snap it back on, so I'm guessing that your clips are loose or broken. I had thought about installing an upgraded leather shift boot until I read this whole installation procedure, and told myself I just knew I was going to break something doing it, so I decided to keep the stock one.