  Topological charge pumping occurs in the adiabatic limit, and the
non-adiabatic effect due to finite ramping velocity reduces the pumping
efficiency and leads to deviation from quantized charge pumping. In this work,
we discuss the relation between this deviation from quantized charge pumping
and the entanglement generation after a pumping circle. In the simplest
setting, we show that purity $\mathcal{P}$ of the half system reduced density
matrix equals to $\mathcal{R}$ defined as $(1-\kappa)^2+\kappa^2$, where
$\kappa$ denotes the pumping efficiency. In generic situations, we argue
$\mathcal{P}<\mathcal{R}$ and the pumping efficiency can provide an upper bound
for purity and, therefore, a lower bound for generated entanglement. To support
this conjecture, we propose a solvable pumping scheme in the
Rice--Mele--Hubbard model, which can be represented as brick-wall type quantum
circuit model. With this pumping scheme, numerical calculation of charge
pumping only needs to include at most six sites, and therefore, the interaction
and the finite temperature effects can be both included reliably in the exact
diagonalization calculation. The numerical results using the solvable pumping
circle identify two regimes where the pumping efficiency is sensitive to
ramping velocity and support the conjecture $\mathcal{P}<\mathcal{R}$ when both
interaction and finite temperature effects are present.
