I had a bunch of birds nest fungi come up in my organic compost. Tried to scrape them out but they kept coming up. Tortoise never ate them and no bad effects. You might try to identify what type of mushrooms they are by looking on the internet to find out if it is toxic or not.
I have had some come up in the past, I agree to try and identify it is probably best, I usually trust that the torts will know what is good for them. Their hyphae will be all through the substrate so if you want to get rid of it you will have to change your conditions or take all the substrate out and replace it or cook it, also wash out the container.