Orange paint was used in an attack on the cottage at Alt Na Reigh in Glencoe at the weekend.
The incident follows similar attacks last month, when stones were thrown at the cottage and "Jimmy the beast" was written on a wall.
Councillor Andrew Baxter suggested the local community might want the property to be demolished.
TV presenter Savile, who died last year at the age of 84, is currently the subject of investigations into allegations he abused hundreds of young girls and some boys over a period of forty years.
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Savile was knighted in 1996 and bought the Glencoe cottage in 1998.
His charitable trust had initially planned to convert it into a respite centre for the disabled, but its sale was halted earlier this year following the allegations.
The charity has announced it will close down.
Mr Baxter told BBC Radio Scotland the cottage was in a prominent location in Glencoe and there was a worry it had become the focus for the anger directed at Savile.
He said: "There has been lots of talk of alternative uses such as a respite centre, or perhaps a mountain centre to get disabled people into our hills.
"But I feel rather uneasy about some of those options especially considering some of the revelations we have seen in recent weeks.
"If it was the opinion in the local community but to erase the memories of Savile in the glen then perhaps demolition is the only option."
(IT)
