Removing excess grout

I only know of two ways to remove grout: 1. scrape 2. acid

Travertine is a form of calcium carbonate and acid would eat it as well as the grout. Calcium carbonate is also very soft and can easily be scratched/damaged by scraping with steel.

I don't know what you mean by "adjusted to the edge area of the travertine tile" but I'd try a wooden scraper. Hard wood.

Sorry for confusion, here is what happened: while applying some fresh grout over a seam (to fix a wrong colored stretch) it was pasted over the adjoining tiles.

Would using even fine sandpaper lead to the surface damage as well?

On ceramic tile, vinegar in water is used to remove fresh grout haze. On marble, vinegar might affect the gloss. I would first try a marble cleaner - follow label instructions. A non-abrasive plastic scrubber or stiff nylon brush would probably help without scratching marble. Your question is confusing. Is this polished? Tumbled? Floor? Large area?

I did a google search on "travertine remove grout haze" - lots of hits, including commercial products:

I have been working with my Travertine for 20 years. The only way I can think of fixing the situation would be to get a good supply of razor blades and a blade type scraper and carefully scrape off the excess. If you are careful and use the proper angle, you may be successful. NO NO acid or vinegar, etc. The Travertine is very soft compared to other stones and will etch quickly with any acid.