The photo shows the painting as it hung at the salon of '84 with the strap off her shoulder -- much more daring.  

After the show, John repainted the strap to its present position. This, apparently, had gone unnoticed in the english literature for close to a hundred years until the art scholar Trevor Fairbrother discovered it in this old photograph depicting the Salon. What an AMAZING discovery! and in many ways totally alters the appearance of the image -- at least in the coquettish nature of Mde. Gautreau. 

With Sargent repainting the strap, he successfully (though I might add somewhat ruinously) took much of the sting out of the painting. 

Why did he do it? 

The onslaught of Gautreau's mother certainly must have played a part. He was clearly  caught off guard by the public's reaction which you can read in the letter from Ralph Curtis to his family. He had gone too far -- or so he must have come to think.

What a shame that the legacy we now have is but a self censored version of the original for I'm convinced his first instinct was the better one.

To see how the painting might have looked, take a look at an altered image done by Mike Pieczonka:

Madame X - as she might have originally been painted

Note