  In this note, we are interested on the event of extinction and the property
of coming down from infinity of continuous state branching (or CB for short)
processes with competition in a L\'evy environment whose branching mechanism
satisfies the so-called Grey's condition. In particular, we deduce, under the
assumption that the L\'evy environment does not drift towards infinity, that
for any starting point the process becomes extinct in finite time a.s. Moreover
if we impose an integrability condition on the competition mechanism, then the
process comes down from infinity regardless the long term behaviour of the
environment.
