How can I teleport between games?

I have two games but one I only want to be accessed through the first one. I've tried adding the second game to the first one but it says that it can't have it's start place configured as it's already a start place in a game, but I don't know how to remove it from being a game and turn it into a place. I currently have the second game private, and the first game public.

Here is the code I have in the first game:

local TeleportService = game:GetService("TeleportService")

local placeID_1 = (My second game id is here)

script.Parent.Touched:Connect(function(hit)
    local player = game.Players:GetPlayerFromCharacter(hit.Parent)
    if player then
        TeleportService:Teleport(placeID_1, player)
    end
end)