In the hierarchical formation scenario in which the outer halo of the Milky Way is the result of the continuous accretion of low-mass galaxies, a fraction of the Galactic globular cluster system might have originated in and been accreted with already extinct dwarf galaxies. In this context, we expect that the remnants of these progenitor galaxies might be still populating the surroundings of those accreted globulars. In this work, we present wide-field photometry of a sample of 23 globular clusters in the Galactocentric distance range 10 ≤ RG ≤ 40 kpc, which we use to search for remnants of their hypothetical progenitor systems. Our deep photometry reveals the presence of underlying stellar populations along the line of sight of about half of the globulars included in our sample. Among the detections lying in the footprint of the Sagittarius tidal stream, which we identify via the comparison with its orbit derived from numerical simulations, only Whiting 1 and NGC 7492 seem to be immersed in that remnant at a compatible heliocentric distance. We also confirm the existence of a subjacent main-sequence feature in the surroundings of NGC 1851. A tentative detection of the vast Hercules-Aquila cloud is unveiled in the background of NGC 7006.