I ask them about the history of time travel and either listen to them, or accept the recording they give me, and carefully record it myself. Then I ignore them and try to metagame time travel, assuming they've set up some form of time loop.

The first step is to buy lottery tickets (with choices based on a quantum RNG), and if I win, buy more lottery tickets until I have an arbitrary amount of wealth. If I'm in a time loop, there will exist an iteration where I win all attempted lottery instances (note that only non-deterministic RNGs will work for this, like the one I have on my desk). I then use that wealth and my foreknowledge to adjust the future history of time travel such that I exclusively control the technology. Then I send someone back in time with the recorded history (now incorrect) of time travel.

That ought to destabilize any loop they're trying to set up after a finite number of iterations, and wrap my loop around it. If you're a time traveler looking to prevent me from doing this, I accept cash, money, and filthy lucre. Just make sure the dates on the bills make sense for this period.