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The default cheese is unlikely to produce exactly what you want. For many applications one would like the same sources removed from each detector. Due to the way the emllist.fits file is constructed, and the way region accesses it, this is not a trivial task to program in an automated way. However, it can be done with a small amount of hand editing of the emllist.fits file, if you are willing to learn the details of the emllist.fits file and how it is used by region.
From inspection of the images, determine the FLUX or DET_ML limit you wish to impose. Then remove all of the sources that do not meet that criteria for the combination of instruments. Keep in mind that a source may have different DET_ML in different instruments, and so may get excluded from some instruments but not others. (This can be fixed by editing the emllist.fits file or by using emlfill.) Further, if there is a bright source in a chip gap, you will want to excise it, but it may not have an entry for that detector. In that case, you may need to add a line to the emllist.fits file, making sure that the SCTS column is appropriate. And it should be noted that the fluxes for the summary lines will be NAN if the source falls out of the FOV (or on a CCD gap) for any of the detectors.