Ah yes, the Dreaded fur. Normally this is a case of the substrate bieng too wet or putting a real log in. But as you say it is fake.
Now you can scrape the fur off but you might not get all of it, leaving some left over to start over. You should take the log out and clean it and try to leave the tank a little more dry.
I don't know how dangerous it is but in The Tarantula Keepers guide the author states that some of the fungus that grows in T's cages is not dangerous or at least not dangerous enough to kill your Tarantula.
I however don't know if the "fur" is a type of mould or fungus so I would suggest you clean the "fur" off and take the substrate out if there was fur on the substrate too.
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