I have an old scarf made by Etro in Italy.  One side is your usual
wool an the other side is made of silk.  The silk side has worn thin
and has holes in it.  I contacted Etro and they said they can't repair
it.  I've heard Italian clothing is often a cottage industry so that
there must be some artisans somewhere in Italy who are familiar with
this particular tyoe of scarf and can replace the silk with something
rather similar to the worn out silk.  How can I track down those
artisans and arrange for the scarf silk to be replaced?

Silk deteriorates with time.  Whereever you are, you should be able to
find a store that sells silk similar to that of your scarf.  Maybe you
will have to choose another shade or color that complements the wool.
A seamstress  - if not you, yourself -  should have no trouble
removing the old silk and replacing it.