What is this, and why is it melted to my exhaust manifold?

[Matt Taylor]

The day after having some work done at the dealer, I noticed a burning smell while driving around.

While looking around, I noticed what the arrow is pointing to in the pic below. Is that a breather tube? It either melted itself on to the exhaust, or somebody "right stuff"ed it purposefully.

What is this? (it appears to be a tube that runs back to at least the transmission).

 

[KyleT]

transmission, or t-case breather tube.

i would get it off the exhaust and cut it clean, so that its not pinched off.