What makes time travel "legal" or illegal? Let's start with the simplistic: you go to bed at night, close your eyes and poof, it is eight hours later. Not really time travel? Well, imagine if, instead of falling asleep, you were frozen solid and thawed out 14 centuries later. Still legal, right? So traveling into the future is always legal and creates no time paradoxes. Don't think it could happen? It already did. Some Russian scientists were able to take tissue from a plant that had been frozen for over 30,000 years and get it to grow, thus resurrecting a species 300 centuries old. The plant is still growing and fertile and producing white flowers and seeds. So traveling into the future is a piece of cake.
But traveling backwards in time, that's always a problem. Everyone has heard of the grandfather paradox. You go back in time, kill your grandfather before your father is born, so you were never born, so you could never travel back in time and kill your grandfather. Some authors side-step this with the "multiverse" theory. They allow you to travel back in time, change things and thus create a new timeline. Your original timeline is preserved.
I've never been a big fan of time travel or multiverses. But my characters can travel faster than light. So they can go back in time "observationally" meaning legally. All they are doing is snagging photons that were emitted farther in the past. Thus the starprobes and their lens-less camera are time machines but only in the sense that they can see into the past. They cannot actually travel backwards in time. They can never interact with anything in the past and they can never disturb the one true timeline.