Try cleaning the area with tri sodium phosphate, available at a paint store. It might work.

I wouldn't blame the cleaning woman and blame yourself for picking such a poor material as limestone for a splash material...especially around a kitchen.

Limestone is very soft and made mostly of calcium and will be damaged by all common acids like lemon juice, vinegar, soda, and even acidic water coming from your taps.

Although the repair your DH suggested will work temporarily, be prepared to have this problem reoccur again and again as the limestone gets splashed with acidic solutions.

Manhattan, this is not in a kitchen, it's in a bathroom (as you would have noticed had you checked the picture). I wasn't planning on using any lemon juice, vinegar, or soda in there, plus we have soft water.

FWIW: IMHO there is nothing in that picture that identifies the location as either a kitchen or a bathroom.

That being said muriatic is a powerful cleaner for masonry stains. The attached link offers some alternatives as well as describing muriatic acid.

HTH

Here is a link that might be useful: muriatic acid

I'd be concerned about the fumes from muriatic acid etching the limstone. At least provide plenty of fresh air and expect lots of foam from the acid dissolving the limestone.

You may be able to get a clear, penetrating sealer, such as, but not, silicone, which is used on exterior brick. Contact a marble dealer.

Limestone probably wasn't the best choice for the job, but I'd have to say the original comment was rude.

It was an insensitive comment knowing that you had already installed it. The fact is, however, that limestone is a soft and porous stone that will etch (dissolve) when it comes in contact with anything acidic. Sealers will help with the staining portion but will not prevent etching. Most people who buy limestone recognize that it will get etched and many people like that "worn" look. As I noted in an earlier post, the fact that the grout also appears to have been stained, would seem to indicate that it didn't etch so much as absorb the stain. there are poultices available that should remove that. It is strange that it stained like that even though you put three layers of sealer on.