Can we please stop telling people that time travel will/can cause the object in your hand to change in front of your eyes?
Objects in spacetime follow the path defined by the laws of physics. If you brought an object from your timeline[1] it (and indeed you) will not change to suit the new reality you're in. It will just be an object, like you, stranded from another place, even if the return journey closes because of one of your actions.
The first housecat in Australia just hangs out and eats everything, it doesn't start acting like a koala. (traveling in space and time are the same thing, even though one is more restrictive in which way you can go.)
EDIT: There is another alternative, which is that there is only one causal universe, and it is impossible to change things that happened in the past (e.g. every time you try to kill Hitler you fail, and maybe make him tighten up his security making it impossible for a local-time assassin to do their job, all of which was reported in local documents that you already knew about, or similar.)
[1] or universe, if you believe in multiple possible worlds.