Very carefully! :) And accept that you might not be able to do it. Here's where you pray for a sloppy sub-standard contractor.

How do you know the original marble is under there?

And how was the pink 4x4 laid?

Well, there's a very good chance that the job was sloppy, given that they laid the tiles around the vanity and toilet instead of under them. We know this because we first found the tiles when we had the toilet replaced, and again when DH pulled off the toe-kick on horrible 1960's vanity to see the condition of the floor under it. Aside from a little rust where the original pedestal clearly stood, it looks to be in great condition.

Now the only question is how to get started in pulling up the pink tile. The glue that appears to have been put down first comes right off with a plastic putty knife, but we're having trouble figuring out how to pull up the tiles to even get to the glue layer.

Does anyone have experience with removing a single layer of tile from another layer?

It's very likely that the marble is embedded in a solid mud base and won't easily come loose.

Are the 4x4 pink tiles vinyl or ceramic?

Be prepared to have the marble re-polished.

It is very unlikely to be in good shape, especially after removing tiles adhered to it (thin set or mastic will not matter much).

Marble is soft stuff and easily damaged.