Context. A set of 20 extremely red galaxies at 2.5 ≤ zphot. ≤ 3.8 with photometric features of old passive-evolving galaxies without dust, with stellar masses of 1011M⊙, have colors that could be related to passive-evolving galaxies with mean ages larger than 1 Gyr. This suggests they have been formed, on average, when the Universe was very young (<1 Gyr). Aims: We provide new estimates for the stellar content of these 20 galaxies, with a deeper analysis for two of them that includes spectroscopy. Methods: We obtained, with the GRANTECAN-10.4 m, ultraviolet rest-frame spectra of two galaxies and analyzed them together with photometric data. The remaining 18 galaxies are analyzed only with photometry. We fit the data with models of a single-burst stellar population (SSP), combinations of two SSPs, as well as with extended star formation. Results: Fits based on one SSP do not provide consistent results for the blue and red wavelengths. Moreover, the absence in the spectra of a break at 2 × 103 Å indicates that a rather young component is necessary. Using two SSPs we can match the photometric and spectroscopic data, with the bulk of the stellar population being very old (several Gyr) and the remaining contribution (<5% of stellar mass fraction) from a young, likely residual star formation component with age ≲ 0.1 Gyr. Exponentially decaying extended star formation (τ) models improve slightly the fits with respect to the single burst model, but they are considerably worse than the two SSP based fits, further supporting the residual star formation scenario. Conclusions: The fact that one SSP cannot match these early-type galaxies highlights the limitations for the use of age estimators based on single lines or breaks, such as the Balmer break used in cosmic chronometers, thus questioning this approach for cosmological purposes.