Time travel passwords are vulnerable to mindreading. If you want a good time travel password, you have to have an algorithm which the time-travelling version of you can calculate, but which can't be directly read by a mindreader because if he's reading it right now, he has no time to calculate it. For instance, I can have a time-travel password of "digits 300-310 of the square root of 3". A time-travelling version of me would know the password, so can compute it, then can tell me the result and I can check it. A mindreader would have to read my mind before the fact or engage in some time travel himself.

Of course, it's impossible to have a time-travel password immune to all such tricks (maybe the mindreader did read my mind a week ago), but there's no reason to allow blatant loopholes.