We report inelastic light scattering results on the stoichiometric and fully ordered superconductor CaKFe4As4 as a function of temperature and light polarization. In the energy range between 10 and 315 cm−1 (1.24 and 39.1 meV) we observe the particle-hole continuum above and below the superconducting transition temperature Tc and seven of the eight Raman active phonons. The main focus is placed on the analysis of the electronic excitations. Below Tc all three symmetries projected with in-plane polarizations display a redistribution of spectral weight characteristic for superconductivity. The energies of the pair-breaking peaks in A1g and B2g symmetry are in approximate agreement with the results from photoemission studies. In B1g symmetry the difference between the normal and superconducting state is most pronounced, and the feature is shifted downwards with respect to those in A1g and B2g symmetry. The maximum peaking at 134 cm−1 (16.6 meV) has a substructure on the high-energy side. We interpret the peak at 134 cm−1 in terms of a collective Bardasis-Schrieffer (BS) mode and the substructure as a remainder of the pair-breaking feature on the electron bands. There is a very weak peak at 50 cm−1 (6.2 meV) which is tentatively assigned to another BS mode.