One of the strongest known electron-accepting fragments used in the synthesis of organic dyes for applications in nonlinear optics (NLO) is 1,3-bis(dicyanomethylidene)indane (BDMI). By studying a benzylidene-type push–pull chromophore bearing a 5-carboxy-BDMI electron-acceptor and 4-(dimethylamino)aniline donor fragment, we demonstrate that this class of compounds can show unusual response to the polarity of the surrounding medium. The combined results of UV-Vis absorption spectrometry, NMR experiments and computational modeling indicate that the studied compound undergoes a geometrical transformation that involves an increase in the torsion angle ω between the aniline and indane ring systems with the rise of the polarity of the surrounding medium. This process is partly facilitated by an increased rotational freedom around ω in more polar solvents, as detected experimentally by NMR and predicted by calculations. Regarding the practical application aspects, computations predict that the solvent-polarity-induced increase of torsion ω would lead to a notable decrease in the first hyperpolarizability (β) value. This was detected experimentally, as hyper-Rayleigh scattering (HRS) data showed a drop in the compound's NLO activity from βHRS(532) = 513 × 10−30 esu in toluene to βHRS(532) = 249 × 10−30 esu in acetonitrile. This places limitations on the NLO applications of the studied compound and its structural analogues, as the surrounding medium (solvent of polymer matrix) with the lowest possible polarity needs to be used to maximize their NLO efficiency.