In turbulent premixed flames, not only the isotropy of velocity fluctuations is altered by the thermal expansion effect, the dissipative structure of the turbulent flowfield and the flow topology are also deeply influenced by the flame. Considering the joint probability density function (JPDF) of the second and third invariants of the velocity gradient tensor (VGT)-or its traceless counterpart-is a classical way to educe the topology of turbulent flows at these smallest scales. These quantities are analyzed by considering direct numerical simulation databases of premixed flame kernel growth in homogeneous isotropic turbulence (HIT). Two conditions of turbulence-combustion interaction (TCI) are considered, which correspond to two distinct values of the Bray number. The analysis of the VGT shows that the propagating premixed flame and its associated density variations significantly modify the turbulence structure and flow topology. To understand this behavior as the flow interacts with the flame front, Lagrangian dynamics of the VGT and its invariants are studied by considering the conditional mean rate of change vectors. Special emphasis is thus placed on the Lagrangian evolution equations (LEE) of these invariants. To the best of the authors' knowledge, this is first time that such budgets are scrutinized in premixed combustion conditions. The pressure Hessian contribution to the VGT invariants transport equations is shown to be one of the leading-order terms in this evolution, making it critically important to the flow dynamics and turbulence structure.