A tiled splashback behind a gas hob, I guess is always going to accumulate grease. A standard grout is going to suffer fairly quickly. There are literally dozens of grouts available, but the best thing I can think of would be to include an additive in the mix. That would stop the powdering, and also make the grout much more resistant to grease etc.
It's very specialised today. I'm guessing that your guy has used a proper, standard grout that any DIYer would use........... and used it in all good faith. If so, then a good idea would be to remove it now, and re-grout with something suitable. It's going to depend on his "attitude". That's a depressing thought, I know. Good luck.
Old-fashioned non-setting mastic (if that's what it is) wouldn't be the right seal between cooker and tiles. Modern silicone is usually used now. Once it's cured, no amount of touching or rubbing should disturb it.