Roger, any chance of a picture of the rug in question. You say it is 100% silk but then suggest about jute which has been pointed out shouldnt be there if it is pure silk.
Price wise you may well have a mercerised cotton rug but this wouldnt have jute in either.
Also price wise, if it is a 3ft x 5ft rug and a £1000 chances are it is not silk.
Anyway, dry cleaning is always a safe way of cleaning something just bear in mind it doesnt work.
Best, Dave.