So, we've had mushroom-like fungi growing in this area all year (which is kind of unusual). They don't seem to mind if it's dry and hot, even in bare dirt. They still grow, and fast! They seem to pop up more when it gets wet, though. It's wet right now.
On Saturday, someone pulled some of them up (as apparently they've done more than once), and today, in the exact same spot, there's a big patch of them that look the same! they do get bigger and healthier/different looking than they look now, though.
I personally think these are really cool, and I'd probably just let them grow if it were me.
Here are pictures of the pulled up ones shriveled from the sun, followed by the new ones that I saw this afternoon (two days later):