In "A Sound of Thunder," Ray Bradbury explores how apparently minor changes in the past might create catastrophic changes to the future. With this in mind, Time Safari has set up various safeguards to prevent unintentional contamination of the timeline. For one thing, it has set up a metal path above the prehistoric earth for its time travelers to walk on, with the hunters being warned not to leave it for any reason. As Travis, the safari guide, explains,
It floats six inches above the earth. Doesn't touch so much as one grass blade, flower or tree. It's an anti-gravity metal. Its purpose is to keep you from touching this world of the past in any way.
Additionally, the company is careful to only select animals that would have already died regardless of any time travel. Before the hunters arrived, the company had sent another employee, Lesperance, to track the animals across the course of their lives. As Lesperance states:
When I find one that's going to die when a tree falls on him, or one that drowns in a tar pit, I note the exact hour, minute and second. I shoot a paint bomb. It leaves a red patch on his hide. We can't miss it. Then I correlate our arrival in the Past so that we meet the Monster not more than two minutes before he would have died anyway. This way, we kill only animals with no future, that are never going to mate again.
Indeed, the hunters are barred from taking physical trophies (although they can have a photo taken of themselves standing next to the animal). Finally, the bullets are collected and brought back with them.
In addition, before Eckels travels back in time, he is forced to sign a waiver. In the course of his conversation with the Time Safari employee, we observe the employee trying to intimidate him, testing his nerve. Thus, we read this exchange:
A Tyrannosaurus rex. The Thunder Lizard, the damndest monster in history. Sign this release. Anything happens to you, we're not responsible. Those dinosaurs are hungry.
Eckels flushed angrily. "Trying to scare me!"
Frankly, yes. We don't want anyone going who'll panic at the first shot.
Even before the hunters travel into the past, there does seem to be an attempt to weed out those clients who might be inclined to spook or panic.
Of course, here it should be noted: if this act of intimidation were to be counted as a precaution, it is entirely insufficient, given this is specifically what happens with Eckels himself, who panics when faced with the dinosaur. Additionally, you should keep in mind Travis's own unprofessionalism when, driven by anger, he forces Eckels to return to the dinosaur and dig out the bullets himself. Given the stakes involved with time travel, this is a dangerously reckless action on Travis's part, which only introduces the potential for further contamination of the past.