Chemical interaction between the tips and molecules is one of the main contributing mechanisms to tip-enhanced Raman spectroscopy (TERS). In this work, we calculate the TERS spectra of the biphenylene (BP) dimer at 13 nonequivalent tip sites by means of density functional theory and explore the influence of the TERS tip on vibrational mode characters and Raman intensity. The Raman intensity of the vibrational mode involving the antisymmetric stretching of tetra-rings is found to be specifically enhanced. We attribute this specific enhancement to the electronic sensitive atom vibrational character of the mode and infer that the vibrational strength of atoms can be tuned by the TERS tip. The results provide an intuitive interpretation on the effects of tip-induced electronic redistributions on specific vibrational modes in TERS and indicate the possibility to further improve the TERS resolution.