What is the simplest way to have a script remove its self after an "onTouch" function?

The simplest way is not to remove it but to disable it script.Disabled=true think about it.

Simplicity is not equal to Efficiency.

The simplest, and probably most efficient way to make an event not activate more than once would be to use the disconnect method.

To do this you need to make a connection( i.e. connection statement ) and tie it to a variable. Then, you can use the disconnect method after the definition of your function.

local connection --Define it before, so it doesn't return 'nil' inside itself.

connection = p.Touched:connect(function(part)
    local plr = game.Players:GetPlayerFromCharacter(part.Parent)
    if plr then
        wait(.5)
        PlayerIsFound.PlayerGui.ScreenGuitycoon.TextButton.Visible = true
        wait(1)
        PlayerIsFound.PlayerGui.ScreenGuispawn.TextButton.Visible = false
        connection:disconnect() --disconnect the connection
    end
end)

The easiest way to get rid of something is to just use the Destroy method.

Like so:

game.Workspace.Part:Destroy()

Modified script:

local p = script.Parent


function onTouch(part)
    local HumanoidIsFound = part.Parent:FindFirstChild("Humanoid")
    local PlayerIsFound = game.Players:GetPlayerFromCharacter(part.Parent)
    if HumanoidIsFound and PlayerIsFound then
        wait(.5)
        PlayerIsFound.PlayerGui.ScreenGuitycoon.TextButton.Visible = true
        wait(1)
        PlayerIsFound.PlayerGui.ScreenGuispawn.TextButton.Visible = false
    script:Destroy--Added this
    end
end

p.Touched:connect(onTouch)

There other ways to remove stuff but this is the most straight-forward way.