[genthree]

"Mushroom hunting" is a fairly common phrase in English, too. It appears to have the top-level title for the page about that activity, on Wikipedia, even (mushroom foraging, mushroom picking, and mushrooming are all given as alternative terms)

Plus it's the title of a song on the Cowboy Bebop soundtrack, so it has that going for it.

[peterlada]

Sadly a missed opportunity for calling it mushroom pilfering.

[euroderf]

Or mushroom requisitioning. Or mushroom commandeering. Or mushroom pillaging.