The answer is that the number of iiterations must be increased. Using the following code
Inpaint[img, Dilation[Binarize[img, {0.9, 1}], 1], Method -> #,
MaxIterations -> 1000] & /@ { "Diffusion", "NavierStokes",
"TotalVariation"}
I am obtaining the following results
It is observed that now, the "total variation" is performing better than "diffusion" and "Navier Stokes".
