Don’t know about a scarf, but I do know that they found a shoe from Earhart’s era on some little islet in the area where she should have gone down. Of course, there was no evidence that it belonged to Earhart.
The book "Finding Amelia" has, in its Epilogue, a telegram sent by Officer in Charge G.B. Gallagher (shown at above site), which left me with the impression that Amelia's remains had been found and nobody followed up on it. Read the five pages on that site for the full info.
Interesting stuff.