Any ideas on how to undo this?

As I suspect you already fear the only reliable way to deal with this is to go back to bare wood and then finish again. Since you used an oil finish blending the new finish back in with the old should be possible (this is frequently given as one of the main selling points with oil finishes of all kinds).

Unfortunately this may not be a simple matter of just spot-sanding/scraping the affected area because the stain might have penetrated deeply enough that you will create a visible low spot. You'll have to be guided by what you discover once you start to sand or scrape.... you might get lucky :-)

One additional point to note is that the newly worked wood is likely to be noticeably lighter in colour than the wood around it. The colour will even up eventually, but it will take some time and you'll need to be patient.

For both the above reasons you may want to bite the bullet and just refinish the whole surface. I've done this myself more than once to treat localised staining.

Note: oils (and waxes, and all mixtures of them) are relatively poor surface protectors and it can be prudent to embrace minor stains here and there as a natural aspect of the finish choice.

This isn't anything related to your main query but I wanted to include something on it.

Edit: the oil used is a food-safe countertop oil made from "natural linseed oil, sunflower oil, soy oil and carnauba wax".

The "food safe finish" thing is a great con in woodworking circles and does a lot to distract from the truth in this area. In reality it appears one can safely assume that all regular wood finishes are food safe (once fully dried/cured in the case of drying finishes) because there is not, and never has been, any evidence to the contrary.

In practice one of the main takeaways related to this is that there is no reason to prefer a "food-safe" finish over one that isn't sold as such, but which may be a better (and frequently also cheaper) finish.