The coupling between the intermolecular motion and the internal vibrational coordinate in the He-CO system is computed at the post-Hartree-Fock level using the DFT+DISP model already employed by us for similar systems and reviewed here in the main text. The quality of the computation of such weak effects is compared with other, earlier model calculations and then used for the evaluation of the vibrational relaxation cross sections of the CO molecule diluted in He-4 gas. A further assessment of the vibrational coupling is carried out by computing, with a stochastic approach that employs the Diffusion Monte Carlo method, the effects on the vibrational frequency of the CO impurity from its immersion in He-4 droplets of variable size. Both sets of results are analyzed and discussed to gauge the reliability of the computed coupling vis-a-vis one of those suggested by earlier calculations. This study provides further evidence on the difficulty of quantitatively obtaining from calculations the extremely small effects connected with molecular vibrational features in this system and caused by the weak interaction between the title molecule and a quantum solvent like He-4.