  We study the renormalization of the electron-spin-fluctuation (el-sp) vertex
in a two-dimensional Hubbard model with nearest-neighbor (t) and
next-nearest-neighbor (t') hopping by a Quantum-Monte-Carlo calculation. Our
results show that for t'=0, the renormalized el-sp vertex decreases quite
generally with decreasing temperature at all spin-fluctuation momentum
transfers. The suppression of the el-sp vertex results in a substantial
reduction of the effective pairing interaction mediated by antiferromagnetic
spin fluctuations in both the intermediate- and strong-correlation regimes. The
inclusion of a finite t'/t<0, increases the Landau damping rate of spin
fluctuations, especially in the overdoped region. The increased damping rate
leads to smaller vertex corrections, in agreement with earlier diagrammatic
calculations. Still, the vertex correction reduces the spin-fermion vertex, as
at t'=0.
