At first, I wasn’t sure what this one was trying to say about the POV character. Is this person an expert time traveler, or an expert on time travelers? This shows (again) why word order matters, because the first sentence seems to say the POV character is an expert on time travelers, but the rest of the paragraph doesn’t support this… ‘Course, time-traveler expert needs a hyphen, as does time-travel expert (an expert on time travel itself, rather than an expert on people who travel in time). Saying expert time traveler would make the hyphen unnecessary, but the meaning is subtly different from (not different to or different than!) time-travel expert; this variation implies “in the field” experience, so to speak, rather than just a lot of knowledge of the physics behind how it works. All things considered, this is the most likely interpretation of what the writer meant to say.
In the second sentence, change legacy to legacies. (More than one person means more than one legacy, unless it’s a single legacy shared by all of ’em, which makes no sense in this context.)
Change farther to further. (Quick way to remember which to use: farther is for literal distances, and further is for figurative. Since time is not space — shut up; we’re here to discuss grammar and punctuation, not vaguely understood concepts of Einsteinian physics — distant times are further away, not farther.)
Add a comma after further into the future.
You can add a comma after One day, but you don’t have to. (Introductory phrases of three words or fewer don’t require commas, but you may want to use them anyway for clarity.)
The last sentence in this example… I know what it’s trying to say, but the word choice/order is a bit wonky, and the easiest way I can think of to fix it is to rewrite the sentence completely.
While we’re at it… Once the person in question is at a funeral home, they’re well past needing any services from a time traveler, ’cause they’re dead. Perhaps hospice is a better word here. (This is another example of why you should never rely solely on grammar programs to catch all the glitches in your manuscript: Grammarly wouldn’t have noticed this problem, nor would have the Hemingway app.)
You’re an expert time traveler working at a hospice. You take dying people into the future, for a price, to see their legacies. The further into the future, the higher the price. One day a billionaire offers you his entire fortune to take him as far as you can into the future.