I'm currently watching the TV adaptation of The Peripheral. I haven't read the book. I've watched the first ~4 episodes.
The time travel technology seems to run both forward and backward in time, and it only works for information, not physical objects. When you do backward time travel and interfere with the past, a paradox is avoided because the universe branches off into an alternate timeline. Once such a branch ("stub") has been intentionally created, you can continue to do VR travel back and forth between the two branches.
So given the description above this seems to be a fairly logical time-travel setup compared to a lot of what you see in SF.
But there is one big thing that doesn't make sense to me at all, at least based on what's been revealed so far. In dramatic terms, the story is presented as if the 2030 North Carolina and 2100 London are just two different sets of scenery. Call them timeline NC and timeline L. The presentation of the story is as if there is some kind of fixed 70-year offset between NC and L, as if the timelines are two rulers, and we've simply laid them side by side and then slid one by some fixed amount. If 3 days go by in NC, then it's as if exactly 3 days are simultaneously going by in L. Therefore it seems like, because of the fixed offset, people in L aren't able to do things like foreseeing the outcome of their own actions in NC, which would kill the drama.
Is this right? I can actually think of several ways of trying to make sense of this.
a fixed offset, as above
Every visit to the past creates a new fork in the timeline, and thinking of it as a single "stub" is just a way of talking (in-world) and a way of doing the dramatic presentation.
The whole thing isn't actually going to make sense at this level, and you just have to suspend your disbelief in the logic.
As an argument against interpretation #2, it's revealed ca. episode 4 that the evil Klept guy had existential unease with knowing that he and his family also existed in the stub. Therefore he had the stub copies of himself and his family killed off. Under interpretation #2, this would not make sense, because the massacre would just create a new fork in the timeline, but it wouldn't get rid of the first stub, where the copies would still exist.