How to create a faded image using an existing image file

You could try something like this:

with your image,

img = Import[""]

create some random noise and smooth it, to make the "dirt grains" smoother:

noise = ImageAdjust[
  GaussianFilter[RandomImage[{0, 1}, ImageDimensions[img]], 2]]

enter image description here

Then binarize that noise, using MorphologicalBinarize:

binary = MorphologicalBinarize[noise, {.6, .7}]

enter image description here

This produces fewer, larger "grains" than simply using Binarize.

Now subtract that image from the alpha channel in your image:

SetAlphaChannel[img, ImageSubtract[AlphaChannel[img], binary]]

enter image description here

You can play around with the filter size and the binarization thresholds to get different "graininess":

rnd = RandomImage[{0, 1}, ImageDimensions[img]];
    ImageAdjust[GaussianFilter[rnd, s]], {t1, t2}]]],
 {{s, 2}, 0, 10}, {{t1, .6}, 0, 1}, {{t2, .7}, 0, 1}]

enter image description here

Given that your image already has an alpha channel, I would try to reduce the opaque mask on the "stamp" that already exists by multiplying the alpha channel by some selected noise.

Here are a few examples:

im = Import[""];

Create flatly random noise in a size half that of the image, then scale. This rescaling reduces pixelation and helps to remove sections rather than just one-off pixels:

ColorCombine[ColorSeparate[im]*{1, 1, 1, ImageResize[RandomImage[1, {100, 100}], {200, 200}]}, "RGB"]

alpha x a resized random image

This one is going to use isolated pixels, but has good contrast since it's using SaltPepper noise:

ColorCombine[ColorSeparate[im]*{1, 1, 1, ImageEffect[ConstantImage[White, {200, 200}], {"SaltPepperNoise", 1/3}]}, "RGB"]

SaltPepper holes in the alpha mask

I think my favorite is a resize of GaussianNoise:

ColorCombine[ColorSeparate[im]*{1, 1, 1, ImageResize[ImageEffect[ ConstantImage[White, {100, 100}], {"GaussianNoise", 2/3}], Scaled[2]]}, "RGB"]

Resize a gaussian noise addition to make it look like regions and not just pixels are missing.

Of course you can play with the noise type and the starting image size to get what matches what you want best.