Lateral correlations along hydrophobic surfaces whose separation can be varied continuously are measured by x-ray scattering using a modified surface force apparatus coupled with synchrotron radiation, named SFAX. A weak isotropic diffuse scattering along the equatorial plane is revealed for mica surfaces rendered hydrophobic and charge neutral by immersion in cationic surfactant solutions at low concentrations. The peak corresponds to a lateral surface correlation length ξ≈12 nm, without long-range order. These findings are compatible with the atomic force microscopy imaging of a single surface, where adsorbed surfactant stripes appear surrounded by bare mica zones. Remarkably, the scattering patterns remain stable for gap widths D larger than the lateral period but change in intensity and shape (to a lesser extent) as soon as D<ξ. This evolution codes for a redistribution of counterions (counterion release from antagonistic patches) and the associated new x-ray labeling of the patterns. The redistribution of counterions is also the key mechanism to the long-range electrostatic attraction between similar, overall charge-neutral walls, reported earlier.