  The extinction transition in the presence of a localized quenched defect is
studied numerically. When the bulk is at criticality, the correlation length
diverges and even an infinite system cannot "decouple" from the defect. The
results presented here suggest that, in 1+1 dimensions, the critical exponent
$\delta$ that controls the asymptotic power-law decay depends on the strength
of the local perturbation. On the other hand, the exponent was found to be
independent of the local arrangement of the defect. In higher dimensions the
defect seems to induce a transient behavior that decays algebraically in time.
