This was a gift from my sister and is a solid science fictiony quote – one that I’m quite happy to put on my wall1.

Being a fan of, but hardly an expert on HG Wells2 and being a fan of, but hardly an expert on the history of science, I had to wonder if this quote was actually from HG Wells’ The Time Machine, or was from one of the movie adaptations. As you will see, this is an easy question to answer. The trick is figuring out why you might want to ask the question in the first place.
HG Wells was brilliant and reasonably familiar with scientific research. To pen that line, he would also need to be a time traveler himself.
The Time Machine was first published in 1895. DNA, or more properly what we now call chromatin (the combination of DNA and its associated proteins) was first discovered in 1868 by Friedrich Miescher. At the time, it was called “nuclein”. The term deoxyribonucleic acid or DNA may have been used by the time HG Wells was writing. The idea that DNA has a “sequence”, however, was not understood until 1919. Critically (both for this quote and the history of modern biology), good evidence that DNA was the molecule that stores genetic information did not exist until 1943.
If HG Wells could not have written this line, who did?
The Internet is very good at answering these questions. If you search for the quote, you will pretty quickly be directed to the IMDB quotes page for the 2002 film The Time Machine starring Guy Pearce. Indeed, neither “DNA” nor “re-sequence” appear in the text of HG Wells’ The Time Machine.
The threat to re-sequence your DNA is a threat that would make sense to the audience of the 2002 The Time Machine remake (of the 1960 original adaptation); but it would not have meant anything to the Time Traveler. He probably would not have known the acronym DNA, certainly would not have known it had a sequence, or been aware of why reordering it would be important.
Of course, in 2005 (the purported year in which the quote was uttered, in the copy of the script I could find3), threatening to re-sequence someone’s DNA really meant that you were going to spend several million dollars chemically identifying the sequence of their DNA and years painstakingly matching it up to a draft, reference genome from the Human Genome Project. In which case, it is not exactly clear who is being threatened.

I think we can safely say that, if HG Wells was aware that the genetic information of an organism was encoded in the sequence of DNA, Dr. Moreau’s process of animal “humanization” would have been written quite differently.
NOTES
1. Of course, this is a pretty empty threat to my children because the most negative impact of re-sequencing their DNA would be to dramatically reduce my own genetic fitness. Second most negative. The most negative would be the reduction of my wife’s genetic fitness and my subsequent relocation to the “dog house”.
2. I’m also a fan of Jaime Murray’s gender-bent, super agent HG Wells from Warehouse 13.
3. I have only watched about three minutes of the 2002 film and did not see the scene in which the quote appeared (for which I can hardly be blamed as the film is not on Netflix, and only garnered a 5.9 at IMDB and a 29% at Rotten Tomatoes – the 1960 version got a 76%).