Am I checking if player owns Gamepass properly?

Answer: Use remote events and check for the gamepass in server. Step 1: Add a remote event in ReplicatedStorage. Step 2: Add a server script in ServerScriptService. Step 3: Write this in the server script:

local MarketplaceService = game:GetService("MarketplaceService")
local WalkSpeedId = (gamepass id here)
local RemoteEvent = game.ReplicatedStorage:WaitForChild("RemoteEvent")

game.Players.PlayerAdded:Connect(function(player)
    RemoteEvent:FireClient(player, MarketplaceService:UserOwnsGamePassAsync(player.UserId, WalkSpeedId)
end)

Step 4: Write this in the local script in a text button:

local RemoteEvent = game.ReplicatedStorage:WaitForChild("RemoteEvent")

RemoteEvent.OnClientEvent:Connect(function(bool)
    script.Parent.Visible = bool
    shouldBeVisible = bool
end)

Step 5: Do a while true do loop in the server script's PlayerAdded function to fire to the client about the visibility of the TextButton:

game.Players.PlayerAdded:Connect(function(player)
    -- replace the `:FireClient()` with a `while true do` loop firing to the client about the client's visibility
    while true do
        RemoteEvent:FireClient(player, MarketplaceService:UserOwnsGamePassAsync(player.UserId, WalkSpeedId)
        wait(2)
    end
end)

Explanations: This is for exploit-proofing. Do the check in the server and fire it to the client in regular intervals to prevent exploiters from opening the TextButton and to annoy them into not opening it anymore (strategy may not work). Hope this helps!

Is this a good way to do it? This way is absolutely fine, HOWEVER checking if they own the gamepass on the server would prevent some exploiters. (Use remote events!)

Can hackers change this so that even if they don't have the gamepass, they can still make the gui visible? Yes most definitely, you cannot stop this though.

Can I use remote events here? See answer 1.

If yes, then how? Make a remote event in ReplicatedStorage, fire it from the server to the client using :FireClient(player). See more here.