Failing to find Lewis in the past, and finding traces of another time machine, Bowler and Doris return to the future hoping to find Lewis and persuade him to show them how to operate the Memory Scanner. This is a bit problematic, because we do not know when, if ever, Bowler would have left the past had Wilbur not taken Lewis to the future. On the other hand, most of what Bowler has done since Wilbur arrived has involved reacting to Wilbur's presence, and so this is simply another change made by Wilbur, whose impact as we have already seen was disastrous.
Once back in the future, Bowler attempts several less than entirely clever ideas to attempt to capture Lewis. The one that matters from a time travel perspective is that he leaps back into prehistory and captures a tyrannosaurus, which he controls with the mind control technology Doris uses. This makes for both suspenseful and comic moments, but raises the issue of the missing dinosaur. That is, in A Sound of Thunder, great effort was made to ensure that the hunters in the past killed a dinosaur which would have died within minutes anyway, and the trampling of a single butterfly changed the world completely. The impact of removing one tyrannosaurus (a ravenous predator at the top of the food chain) on which individual creatures survive to pass their genes to succeeding generations is difficult to assess, but will certainly matter more than killing one butterfly whose life expectancy was not more than a few minutes as it was. This was a dangerous and serious potential change to history. It is perhaps only the irreverence of the story that obscures the problem; but of course it might have been that that particular dinosaur no longer mattered. It thus falls into the category of potentially disastrous changes to history which fortuitously happened not to matter.
It is significant that while Lewis is in the future he learns the slogan used by his future company, "Keep Moving Forward"; it is more significant that the Robinson family teaches him the important lesson of learning from failure, which by then has become the basis for his success. He would not have learned that as soon, perhaps; but then, he would have succeeded with the Memory Scanner absent Bowler's interference, and so would have been bolstered by his first success and probably learned the lesson in time.
There are worse disasters ahead, though, as the film is really only starting to foul time.