  Several Fe chalcogenide superconductors without hole pockets at the Fermi
level display high temperature superconductivity, in apparent contradiction to
naive spin fluctuation pairing arguments. Recently, scanning tunneling
microscopy measurements have measured the influence of impurities on some of
these materials, and claimed that non-magnetic impurities do not create in-gap
states, leading to the conclusion that the gap must be $s_{++}$, i.e.
conventional $s$ wave with no gap sign change. Here we critique this argument,
and give various ways sign-changing gaps can be consistent with the absence of
such bound states. In particular, we calculate the bound states for an $s_\pm$
system with a hole pocket below the Fermi level, and show that the nonmagnetic
impurity bound state energy generically tracks the gap edge $E_{min}$ in the
system, thereby rendering it unobservable. A failure to observe a bound state
in the case of a nonmagnetic impurity can therefore not be used as an argument
to exclude sign-changing pairing states.
