Kelly Jones is still unable to explain why she went missing to her father, Ricky, who flew from his Georgia home to be with her on Friday.
She said she cannot remember anything between 8.30pm on the Friday before last and 7.30pm last Tuesday evening when she woke.
She was found inside the rectory at lunchtime on Wednesday and her father visited Glencolmcille and surrounding areas yesterday to get a picture of the desolate scene in which she vanished.
Mr Jones, who hopes to take his daughter back to the US on Tuesday, released a statement through gardai thanking rescuers and other volunteers who helped in the search.
He said: “My daughter Kelly has been fascinated by Ireland and Irish culture since she was about eight years old.
“She has visited Ireland three times now. This story is not about Kelly, but about the Irish people and what they have done for Kelly and her family and friends.”
Mr Jones also thanked US embassy officials, gardai, Donegal Mountain Rescue and Killybegs Cliff and Rescue teams, as well as the Coastguard and local volunteers.
He added: “They wouldn’t quit until they found Kelly.”
Ms Kelly, 41, was found in distressed condition on Wednesday on a couch in the old rectory, which is now a holiday home.
A search costing €50,000 took place between Sunday and Wednesday.
More than 120 volunteers were joined by the Coastguard helicopter and the search area included the 601-metre-high Slieve League, which has a sharp drop to the sea.
Ms Jones was found less than 600 metres from the search HQ on the Glencolmcille GAA pitch.
As yet, no one has been able to establish where Ms Jones sheltered but it is assumed she must have been indoors.
Rescuers who combed the grounds of the rectory last Sunday and Monday maintain there was no sign of anyone in the grounds at that stage.
Gardai have established Ms Jones has a history of depression, dating back several years, and she has been undergoing psychological assessment in Sligo.