Sounds like a nightmare, and a customer that you might want to pass up
on.  Try spilling a little shellac on their carpet and see how fast
they want you to take the mechanism to your workshop to work on.  If
you want to be nicer, then show them the materials that you work with
and explain that they often spill and you want to protect their
carpets/floors/etc.

I don't know how far you've already got into the job, but if they still
insist, you can at least make it worth your while.  Explain to them the
cost difference if you do it all at your workshop vs. doing it all
at the home (your setups, workbenches arranged) and that this costs you
time which translates to his $$$s.

(A friend of mine has a sign in his workshop:
  Shop rate:    $20/hr.
  If you watch: $40/hr.
  If you help:  $80/hr. )

Hope that you can still do something about it...

Eliyahu Shahar