The man behind the desk says he does not guarantee they will come back alive.
Eckels is a tourist. He is not just any tourist though. He is a very rich tourist. He has been a big game hunter for quite some time, and he wants a bigger challenge. For this challenge he has gone to Time Safari, Inc. They are a very unusual travel agency. They will take you anywhere in the world, to any time in the world—for a fee.
When Eckels asks the man behind the desk if the company will guarantee that he “come back alive” he is told the following.
"We guarantee nothing… except the dinosaurs… This is Mr. Travis, your Safari Guide in the Past. He'll tell you what and where to shoot. .... If you disobey instructions, there's a stiff penalty of another ten thousand dollars, plus possible government action, on your return."
This is not a very comforting thought. He is paying big bucks to go on this safari, to shoot a Tyrannosaurs Rex. Then he is told to sign a release, because “Anything happens to you, we're not responsible.” For this he paid ten thousand dollars.
Travis told him that they lost six safari leaders. Perhaps it was because the safari goers were idiots who did not do as they were told, and stepped off the path. Travis is very specific about the path, but Eckels panics when he sees the dinosaur. He is supposed to be a great hunter, but a dinosaur is like nothing he has never seen.
"It can't be killed," Eckels pronounced this verdict quietly, as if there could be no argument. He had weighed the evidence and this was his considered opinion. The rifle in his hands seemed a cap gun. "We were fools to come. This is impossible."
In his hesitation and fear, he steps off the path and accidentally kills a butterfly. He brings it back to the future on his shoe as evidence. Travis is angry when he realizes that one man in his stupidity has altered the course of humanity.
See how the incident is foreshadowed, from the sign at the beginning of the story, to Eckels asking if they can guarantee his safety? The great irony of it is that he wasn't killed by a dinosaur, he was killed by Travis.
Bradbury shows us the “Butterfly Effect” in all its science fiction glory with this allegorical story. One small incident can have far-reaching effects that you can never predict. The farther back into time you go, the greater the effect. It is a good reason never to invent a time machine!