Embrace the patina!

Or get a marble restoration company to come and clean them up and then use a better sealer.

Do you have any photos?

Embrace the Patina

Stained Marble

Thought i posted with original comment but here is a pic

The good news to me is that it is not terrible. We marble owners have to expect things are going to be more lived in, worn looking and used. A kitchen that a cook lives in and enjoys working in. Marble kitchens have been around for hundreds and hundreds of years. Cooking with oil, butter, wine, lemon and spices can cause some stains. Yes there is some staining and discoloration. I am sorry you are disappointed maybe a stone guru can chime in.

You said you tried a poultice, How long did you keep it on? I found this info below that might help you.

Natural Stone Institute

OIL-BASED
(grease, tar, cooking oil, milk, cosmetics)
An oil-based stain will darken the stone and normally must be chemically dissolved so the source of the stain can be flushed or rinsed away. Clean gently with a soft, liquid cleanser with bleach OR household detergent OR ammonia OR mineral spirits OR acetone.

Poultices

Making and Using a Poultice
A poultice is a liquid cleaner or chemical mixed with a white absorbent material to form a paste about the consistency of peanut butter. The poultice is spread over the stained area to a thickness of about 1/4 to 1/2 inch with a wood or plastic spatula, covered with plastic and left to work for 24 to 48 hours. The liquid cleaner or chemical will draw out the stain into the absorbent material. Poultice procedures may have to be repeated to thoroughly remove a stain, but some stains may never be completely removed.

Poultice Materials
Poultice materials include kaolin, fuller's earth, whiting, diatomaceous earth, powdered chalk, white molding plaster or talc. Approximately one pound of prepared poultice material will cover one square foot. Do not use whiting or iron-type clays such as fuller's earth with acid chemicals. The reaction will cancel the effect of the poultice. A poultice can also be prepared using white cotton balls, whitepaper towels or gauze pads.

Cleaning Agents or Chemicals

OIL-BASED STAINS
Poultice with baking soda and water OR one of the powdered poultice materials and mineral spirits.

ORGANIC STAINS
Poultice with one of the powdered poultice materials and 12% hydrogen peroxide solution (hair bleaching strength) OR use acetone instead of the hydrogen peroxide.

IRON STAINS
Poultice with diatomaceous earth and a commercially available rust remover. Rust stains are particularly difficult to remove. You may need to call a professional.

COPPER STAINS
Poultice with one of the powdered poultice materials and ammonia. These stains are difficult to remove. You may need to call a professional.

BIOLOGICAL STAINS
Poultice with dilute ammonia OR bleach OR hydrogen peroxide. DO NOT MIX AMMONIA AND BLEACH! THIS COMBINATION CREATES A TOXIC AND LETHAL GAS!

Applying the Poultice

Prepare the poultice. If using powder, mix the cleaning agent or chemical to a thick paste the consistency of peanut butter. If using paper, soak in the chemical and let drain. Don't let the liquid drip.

Wet the stained area with distilled water.

Apply the poultice to the stained area about1/4 to 1/2 inch thick and extend the poultice beyond the stained area by about one inch. Use a wood or plastic scraper to spread the poultice evenly.

Cover the poultice with plastic and tape the edges to seal it.

Allow the poultice to dry thoroughly, usually about 24 to 48 hours. The drying process is what pulls the stain out of the stone and into the poultice material. After about 24 hours, remove the plastic and allow the poultice to dry.

Remove the poultice from the stain. Rinse with distilled water and buff dry with a soft cloth. Use the wood or plastic scraper if necessary.

Repeat the poultice application if the stain is not removed. It may take up to five applications for difficult stains.

If the surface is etched by the chemical, apply polishing powder and buff with burlap or felt buffing pad to restore the surface.

WOW 5 applications. That is going to be challenging. Hang in there maybe someone else has a better idea. Here are some other links that might have ideas.

Pre Seal oil stain on marble need poultice

(They needed a fan to dry out the stain after the poultice)

Marble stain made bigger

tryin to calm down for an hour about stain on marble

Staining marble countertops

marble cleaner poultice