Reasoning

Classic logical issue. The cause of this claimed "random" deletion isn't random. You see, the while loop has defined Label as the reference to the TextButton it created. Therefore when using Label.Text, which should preferably be Label.Name, it isn't saying "Destroy the clicked Button", it actually is saying, "Destroy the clicked button I just made". Another potential issue is with matched Names. The Listener is asking to find the Label of it's Name, which there likely would be copies. It would end up Indexing the very last one of it's Name, instead of the copy clicked.

Solution

Instead of using a Listener inside of your loop, create another loop traversing through the existing labels. This will allows you to check over every Label for a Click Signal. Though this wouldn't work as the while loop would be running, yes? Well, we can wrap the loop in a spawn as you had done inside, though it was incorrectly used, so please remove it, and it's nested Code.

local ReportedPlayers = Player. -- Pathway to ReportedPlayers | Use as shortcut.

spawn(function()
   while true do wait(1) --// Better do do it like so.
      --// Label creation
    end
end)

for Label = 1,#ReportedPlayers:GetChildren() do
  ReportedPlayers:GetChildren()[Label].MouseButton1Click:Connect(function()
      Label:Destroy()
   end)
end

Hope this helps! If so, don't forget to accept this answer!, and optionally upvote:)

Try naming the button within the script and then deleting it. It will know which button to destroy.