@MadMax - You can remove yourself from challenges.  If you use the website version of Strava, select the "challenges" tab on the top of the page.  As you move your mouse over the box below each challenge where it says "challenge joined", it will highlight to say "leave challenge".  Just click that and you are out of that challenge.  Repeat for each challenge you do not want to be part of.  On the mobile app, go to the list of challenges from the "groups" tab at the bottom.  Just click on the checkmark under the challenge you don't want to be part of and it will remove you from it.

OMG thank you @anchskier I have never been able to figure this out and it's doing my head in 😂

@anchskier  Hey, I was wondering if there was a way to remove challenges from your trophies case. I previously joined multiple challenges and I want to delete them from my profile. Is there a way to do so? (I use strava on my laptop not my phone) Thanks!

@JamesBenton - As far as I know, there is no way to remove a trophy from your trophy case.  You can remove yourself from an active challenge before it finishes, but once it is completed, it doesn't appear that there is any way to delete it from your profile.