This paper analyses robustness of pullback and exponential pullback attractors for the non-autonomous thermoelastic plate with p-Laplacian under the Coleman–Gurtin heat theory derived recently by Fatori et al. [J. Diff. Equ. 259, 4831–4862 (2015)]. Moreover, the existence of pullback attractors in the natural space energy with finite dimensionality is proved together with its upper semicontinuity and continuity with respect to the damped parameter α ∈ [0, 1]. Finally, we prove that the related process has a pullback exponential attractor Mexpα and its Hölder continuity on α ∈ [0, 1]. In particular, when the non-autonomous dynamical system degenerates to an autonomous one, the family of robust pullback and exponential pullback attractors become a robust global attractor and a robust exponential attractor, respectively, so the results of the paper deepen and extend those in Fatori et al. [J. Diff. Equ. 259, 4831–4862 (2015)].