Getting rid of cosmic ray neutrons is a ridiculously hard problem that they are going to deal with mostly by looking at how the neutron detection rate varies as they change the distance between the detector and the reactor core.
The most pernicious source for experiments like this are "fireball neutrons" that are generated from a high-energy muon producing an event that blows up a nucleus in the surrounding rock (via an intermediate pion shower IIRC). This gives you a source of neutrons with energies well up into the 100's of MeV, which will merrily pass through metres of shielding, and a few of them are bound to thermalize in the detector, although most will pass right through.
They've obviously run the numbers on all this (these are very well-known problems for detector design) and decided they can discriminate against backgrounds of this type sufficiently well to make the experiment worthwhile, which all else being equal it certainly is: the possibility of putting brane-world theories to the test is simply too delightful to pass up.
The most pernicious source for experiments like this are "fireball neutrons" that are generated from a high-energy muon producing an event that blows up a nucleus in the surrounding rock (via an intermediate pion shower IIRC). This gives you a source of neutrons with energies well up into the 100's of MeV, which will merrily pass through metres of shielding, and a few of them are bound to thermalize in the detector, although most will pass right through.
They've obviously run the numbers on all this (these are very well-known problems for detector design) and decided they can discriminate against backgrounds of this type sufficiently well to make the experiment worthwhile, which all else being equal it certainly is: the possibility of putting brane-world theories to the test is simply too delightful to pass up.