Be very surprised a high street store would have a Silk content carpet....probably more like viscose\rayon blend,
If I would have been cleaning a silk carpet of that size which would have a value of around 20k + if Silk I would charging a couple of thousand pounds with absolutely no guarantee of outcome.
Doubt the nail polish will come off, why aren't they making an insurance claim, if Silk they could choose any flooring they liked in replacement and the LA would be more than happy to accommodate.