Take it elsewhere!

If this is a manual transmission............you don't need to read the
following, but it does sound like the transmission might be toast if the
trans is indeed smoking.  You can find a used one out there.

Is this an automatic?
There are a few rebuilders that can repair/rebuild them.  Not all places can
though so be careful when you choose.
You can also buy an Audi remanned one and have it installed.
Used ones are out there but I would want to check them out if possible
BEFORE purchasing one.
Is this a Quattro?  If not then one from a Passat might work too.

Of course it could just be a seal that is leaking onto the exhaust.  Cheap
repair relatively!  ;-)

JMHO