Is this actually simulating backward time travel? Or is it just doing entanglement? I.e. somehow entangling the state of your "gift" on day 1 with the message y

Is this actually simulating backward time travel? Or is it just doing entanglement? I.e. somehow entangling the state of your "gift" on day 1 with the message you receive later so that when you get the message it collapses the state of the gift to the right one?