We report on the low-temperature thermal expansion and magnetostriction of the single-impurity quadrupolar Kondo candidate Y1−xPrxIr2Zn20. In the dilute limit, we find a quadrupolar strain that possesses a singular dependence on temperature T, ɛu∼H2log(1/T), for a small but finite magnetic field H. Together with the previously reported anomalous specific heat C, this implies a quadrupolar Grüneisen ratio Γu=∂Tɛu/C∼H2/[T2log(1/T)] whose divergence for finite H is consistent with the scenario of a quadrupolar Kondo effect. In addition, we find a singular behavior of the isotropic strain ɛB in zero magnetic field resulting in a divergence of both the volume thermal expansion and the volume Grüneisen parameter. We speculate that this behavior might be also induced by putative Kondo correlations via elastic anharmonicities or static strain disorder.