Imagine a world with time travel, got it? Good.
Now imagine that time has multiple dimensions. Time has its OWN dimension of time, along which it can evolve. This is called hypertime, or "w" (As in w,x,y,z,t).
Now imagine a WH40K style world-government for humanity, that wants history to stay EXACTLY as it is. Time travel is the in-universe equivalent of heresy and any attempts to prevent the presence of our Lord and Emperor are also Treason. When FTL travel is discovered, the TPA is set up to protect history. (This is of course after the Emperor uses it to become Emperor. "After" in the sense of "w" not "t".)
So yeah, laws are made against changing time, and a government agency is set up to make sure there's no time-spirals that could cause instability in the timeline. (Closed Time-Like Curves in relativity look like spirals when you add in the hypertime dimension.)
They can't move or detect ANYTHING that is in the "hyperfuture". They can use probes or whatever to detect anything in spacetime, but not hypertime. Hypertime passes when the events IN time are changed, so as history changes, hypertime progresses. Time is where space evolves, hypertime is where spacetime events evolve and it only makes sense to think of hypertime passing as events in history are changed.
The Questions are:
How do you detect time travel?
What is the simplest way to have a time agency keep a record of the "TRUE" history.
What is the least handwavium way to have them detect that they've progressed in hypertime?