They look like Evening Primrose, Oenothera seedlings to me.

Right after I posted that I remembered that there is another kind of Oenothera, Sundrops, that is just awfully agressive. I planted it back when I first moved in here 15 years ago and let it go for a couple of years before I realized what a thug it was. It took 3-4 years to get rid of, but it's gone now. I would try to dig out as much of the root system as possible and spot treat anything that came up after that. And move your bunchberry to a new location, poor thing. Good luck!

Funny, I remember trying to establish Oenothera in my perennial garden many years ago and it didn't like it here. I think it was the pink one.

Wonder how this thug got here. The area is relatively undisturbed. Oh some roadside trees got removed a couple of years ago. I wonder if some new sun contributed.

They are not Oenothera fruticosa seedlings. O. Fruticosa has a tight clump rosette type basal foliage pattern, and this looks like it does not. They could be another kind of Oenothera since I've not grown others and can not say, but they actually look like Epilobium seedlings to me which also show up with a vengeance.
Remy

Googled Epilobium foliage and that looks it has a whorled upright habit. This thug of mine seems like a groundcover.

Googling oenethera doesn't get me a good hit either but could be because there are so many species. I didn't look at all of them closely. One phrase that caught my eye though was "nearly stemless". I think that matches mine.