You can replace / update the highscores of the player that's logged in, but it's impossible to remove a highscore in-game. (Because of the way GameMaker Server works, being able to remove any highscore would mean anyone could clear the highscores of any game. That's why I've chosen to only allow replacing/updating your own score programatically.)
Apologies for my delayed responses. As you may know, Outlook is blocking all GameMaker Server mails which means I don't get notified when you post a reply.
On the developer page of your game, there's a link "Dynamic images". You can generate URLs for images with the number of players online and for specific highscores. You can also configure colors & font size.
The ID should be visible on the highscore settings page, but it isn't. If you look at the address bar, you should see something like this: developer/game/xxx/highscores/yyy/. yyy is the highscorelistID. I'll add the highscoreID to the highscore settings page as soon as I can.
I've added the HighscorelistID to the "Edit highscore" page. Please make sure you're calling gms_show_highscore with the right ID. Please also make sure the game is connected to the server by checking gms_info_isconnected.
If you're calling gms_show_highscore before the scores are received they may not be updated properly.
I tested that script and it works just fine too! The issue is with the drag and drop highscore table. Do you think you'll be able to sort it out before the indiesvspewdiepie jam ends? Or could you perhaps show me how to draw my own highscore table with ranks?