Mushrooms in hamster enclosure - How is Tweety?

We found a yellow mushroom in Tweety's terrarium. Through internet research and a conversation with a mushroom and fungus expert, we were able to determine - hopefully accurately - which mushroom it is. Is the fungus dangerous for our hamster? Why do fungi grow in terrariums? What have we done to get rid of the fungus or what do you do against fungus in a hamster enclosure?