We report a systematic dependence of the spin-transfer torque (STT) switching threshold on junction size and its resistance-area product (RA, or rAmtj) for the CoFeB-MgO-CoFeB type of magnetic tunnel juctions. The RA dependence of the switching efficiency is seen to become stronger for junctions of larger size (in the range of 15 to 50 nms). Here, the STT switching efficiency is defined as the ratio of the nanojunction free-layer energy barrier for thermal activation reversal to its STT switching threshold current. That is, the efficiency κ=Eb/Ic0, and it is seen to follow the junction rAmtj in the form of 1/κ=A0+A1/rAmtj, with A1 a-a0, where a is the device diameter and a0 is of the order of 10 nm. The 1/rAmtj dependence is consistent with a tunnel-conductance-dependent spin-pumping-like action, although the spin-pumping mixing conductance originating from the rAmtj of a magnetic tunnel interface is orders of magnitudes below that of the natural damping of the free layer. We postulate that the spin-torque-induced dynamics in these magnetic tunnel junctions must involve high-frequency spin dynamics near the tunnel interface beyond the average free-layer dynamics frequencies. Such interface high-energy process gives rise to a two-step process for spin-current transmission into the free layer and causes visible spin-pumping spin-current loss across a tunnel barrier.