  We report the observation for the p$_{z}$ electron band and the band
inversion in Fe$_{1+y}$Te$_{x}$Se$_{1-x}$ with angle-resolved photoemission
spectroscopy. Furthermore, we found that excess Fe (y>0) inhibits the
topological band inversion in Fe$_{1+y}$Te$_{x}$Se$_{1-x}$, which explains the
absence of Majorana zero modes in previous reports for
Fe$_{1+y}$Te$_{x}$Se$_{1-x}$ with excess Fe. Based on our analysis of different
amounts of Te doping and excess Fe, we propose a delicate topological phase in
this material. Thanks to this delicate phase, one may be able to tune the
topological transition via applying lattice strain or carrier doping.
