When I reupholstered my seat, I took that cover off. It was a pain to get off. I think I weakened the built in clips that snap into the rail on the side of the seat. I got it on but it wouldn't stay in place and sometimes when I sat on the seat it would pop out a little and push the seat button off its stem. I did something creative with a zip tie and haven't messed with it for years.

If I remember right there's 2 clips (like plastic hooks) opposite each other (molded part of the trim piece. They clip into the metal rail somehow. I think mine were spreading apart and allowing it to pop outward. I took a few wire ties linked together and when around the two clips once they were inserted and they keep the clips "squeezed" together. There's also a lateral clip in the end that you have to insert underneath the metal rail (or another trim piece, can't remember) before you push it on. Then I believe there's a small screw on the back. So all in all I think there's 3 molded clips and a screw in the back.

Sorry for the vague description. Going off of memory of about 2 years ago. Just make sure all the clips are there and not broken off or bent. When the plastic is bent it turns white where is was bent back or forth and usually is not as strong as it was.