Will and Hannibal make an awful leap of logic regarding the Chinese symbol etched into a tree. It has many meanings, the most common are that it is the word for "China", and the word for "middle/medium". It is unlikely that 2 professionals would leap to the conclusion of the great red dragon without first considering far more likely answers. However, the fact that it is used on its own and it's evidently a calling card of some sort makes it clear that there is more to the symbol than just its straightforward interpretation.
As Reba touches the fake tiger, you can see through its ear flap. The ear flap is practically transparent.