How do I make a local script in a button recognize if the player has a gamepass?

:UserOwnsGamepassAsync

--- LOCAL SCRIPT

local id = 9581363

    local MarketPlaceService = game:GetService("MarketplaceService")
    local Player = game.Players.LocalPlayer


    function prompt()
        MarketPlaceService:PromptGamePassPurchase(Player, id)
    end
script.Parent.MouseButton1Click:Connect(prompt)


-------------------------------------------

--- SCRIPT, in server script service

    MarketPlaceService.PromptGamePassPurchaseFinished:Connect(function(player, purchaseid, purchasesucess)
        if purchasesucess == true and purchaseid ==  id then
            player:WaitForChild("PlayerGUI"):FindFirstChild("ChangeMaterial", true).Visible = false         
            -- give the player an advantage, like 
        end
    end)

    if MarketPlaceService:UserOwnsGamePassAsync(Player.UserId, id) then
        print("Player already has the gamepass")
        Player:WaitForChild("PlayerGUI"):FindFirstChild("ChangeMaterial", true).Visible = false
    end

You've got a few problems in your script.

First, don't use separate functions when you prompt the player and then deal with what happens after you prompt them.

Second, I'm confused that you set the visibility to false, even though you said that you wanted the button's visibility to be set to true.

Third, PromptGamePassPurchaseFinished is an event, not a function so you would place a period before it, not a colon. You also misspelled "Finished".

Fourth, you do not need to figure out if the player has the game pass by prompting them. I will first show you the correct way to prompt and find out whether or not the player bought the game pass; and then I will show you how to have the game check if the player already has the game pass without prompting them (which is what I think you wanted).

1. When the player clicks on the GUI, they get prompted.

local id = 9581363

script.Parent.MouseButton1Down:Connect(function()

game:GetService("MarketplaceService"):PromptGamePassPurchase(game.Players.LocalPlayer,id) -- prompt player with game pass

-- Now this is after they have been prompted and they either hit cancel or purchased the game pass
game:GetService("MarketplaceService").PromptGamepassPurchaseFinished:Connect(function(game.Players.LocalPlayer, id, wasPurchased) -- wasPurchased is a bool value which tells you whether or not the player purchased the game pass. So if the player hit cancel, the value is false. If the player buys the game pass, then the value is true.

    if wasPurchased == true then -- if player bought the game pass
            script.Parent.Parent.ChangeMaterial.Visible = true
    else
        return
    end
end)
end)

1. When the player clicks on the GUI, the game will check to see if they have the game pass (I think this is what you want).

local id = 9581363
local player = game.Players.LocalPlayer

script.Parent.MouseButton1Click:Connect(function()
    if game:GetService("MarketplaceService"):UserOwnsGamePassAsync(player.UserId, id) then -- UserOwnsGamePassAsync checks if the player has the game pass
    script.Parent.Parent.Visible = true -- I strongly advise you to reference this in PlayerGui instead of StarterGui because it will not become visible until the player resets
    else
        return
    end
end)