You may actually have better luck asking on the kitchen forum. Their are lots of stone/marble enthusiasts there who might be able to help you.

Is the GC taking responsibility for this? Have you confirmed this in writing?

If they are, and have confirmed this in writing etc. then let the GC call the shots - they're on the hook for repairs and if that means replacing your counters, then that's what that means.

As long as whoever is doing the repair work stands behind it and ultimately will reimburse you or replace the counters, then a) make sure it's all agreed in writing and b) let them do what they say they need to do. Ensure that the measure of success is indicated - how much of the stain do they have to remove to be 'good'? What if the spot is still visible be it as a darkened area or difference in the final finish (etched etc).

BTW - your marble counter top is polished? It's not going to stay that way for long. We have 50 sq ft of marble counters in the kitchen (white) and it's honed. More typical for counters as etching isn't as visible. One drop of toothpaste or anything acidic will be a very very visible spot.

An acid won't really help to draw the oil out of the marble, but it will etch away the upper surface of the marble.

I advocate doing the exact opposite:
1) clean the area to get rid of any more surface oil
2) Apply a poultice and cover it with saran wrap. Let it dry. It's the drying action that pulls the oil out of the stone. It may need to be repeated.
3) Then the stone can be repolished if need be.

Again, they are repairing your top and not me. Make your concerns known, but always leave the final action up to them. If you demand they use your methods, then the repair is on you.

I’m having the same issue with plumbers putty staining marble. Any recommendations on the best way to remove the stain? I’ve tried cleaning it with mineral spirits but haven’t had much luck.

I'd waterproof the bottom of the hole, fill the hole full of acetone, cover it with Saran Wrap taped to the deck, and wait a few days. Careful, it's flammable.