Hello Charles.
Travertine is very similar to marble in composition. It is very easily damaged if any solution that is not pH neutral is used on it. The
pine sol msds sheet states that it has a pH of 3-4, which makes it acidic.
Acids will permanently etch the surface. Once the surface is etched, I have found that resealing it or using any of the various supermarket type stone polishes will have no real effect on removing the damage, though there is a temporary improvement in the appearance. The only way to repair damaged/etched stone is to call a specialist who can regrind the stone to remove the etching.
Travertine, marble and other stones are very beautiful, but you have to be really careful with what you use to clean it. The stone experts I have talked to recommend that ¼ cup of Murphy Oil Soap, diluted with 1 gallon of water is highly effective for cleaning and shining the stone without damaging it. This is what we use at Mrs. Clean and I can attest to its effectiveness..
My
cleaning tips for marble might be helpful. I also found some interesting info on travertine:
here