Mike -the tenax traverfill is good-your floor is an unfilled travertine.
The fill that is in there now is the grout the installer used when he grouted the installation.
The holes in their present condition look to shallow to fill-I would hone and clean the surface then seal with MB-24.
You will have to do some explaining to them-it would be easier if you showed them a spare tile they may have of this material-I think it will help them understand what they bought.

On Mon, Feb 13, 2017 at 12:13 PM, Mike Alston <realmikealston@gmail.com> wrote:
Afternoon again, customer has a travertine shower floor with lots of wholes he wants filled in. The shower floor will eventually get wet and I don't want the filled while to reopen. Any suggestions, thanks.

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Stu Rosen