Hard filler (plastic?), and how to get rid of it. Used to seal electronics in place.?

I recently bought a rechargeable toothbrush to learn a little bit more about Induction Power Transfer. But upon looking inside the base unit (the part you set the tooth brush on), I find that it is surrounded by this tan plastic-like stuff. It’s REALLY pissing me off. I can tell that it was poured into the case as a liquid, then it hardened. I have also found this crap inside of a Neon Sign Transformer, with only a small heat sink protruding from the stuff. Is there any kind of easy way to remove this stuff? I spent about 2 hours trying to dig through this stuff, and unintentionally destroyed at least one component. Any suggestions?