[CuriouslyC]

The thing is that there is a lot of variation in ink composition, so it's hard to say universally. That being said, fungi tend to sequester heavy metals in their mycelium, see https://krishisanskriti.org/vol_image/03Jul201502072615.pdf

[dexwiz]

But if you just compost the fungi, you are just back to where you started. With phytoextraction you have to incinerate the plant material afterwards. I know fungi aren’t plants, but similar principle.

[CuriouslyC]

You can harvest the mushrooms and throw them away.

[dexwiz]

The fruiting body of a mushroom often represents only a fraction of total biomass. It depends on the species, but what we see above ground is more analogous to a flower than an entire plant.