According to SAE practices:
From AMS 2430:
3.5.3.1 The amount of metal removed by honing, lapping, or polishing shall be not more than 10%
of the specified minimum arc height for "A" and "C" intensities and not more than 3% of the
specified minimum arc height for "N" intensities

From AMS 2432:
3.6.2.2 For other parts, no more than the equivalent of 10% of the specified
minimum "A" intensity or equivalent "N" or "C" intensity (see 8.5) shall
be removed from the surfaces.

From AMS-S-13165:
I didn't find anything in this spec regarding post peening surface removal.

I'm not sure I comprehend what is meant in AMS 2432. For example, if you used an intensity of .010-.014A then you would be limited to 10% of the lower limit or 10% of .010 or 0.001 inch could be removed. But, if the intensity were in the "N" scale - I'm not sure if you could still remove .001 inch or if you could remove .003 inch since the relation between "N" and "A" intensity is approximately 3:1.