We present results for the $gg$-part of one-loop corrections to recently introduced "topological charge" GPD $\widetilde F(x,q^2)$. In particular, we give expression its evolution kernel. To enforce strict compliance with gauge invariance requirements, have used on-shell states external gluons, and obtained identical both in Feynman light-cone gauges. No "zero mode" $\delta (x)$ terms were foun...