We studied the influence of the populations of neutral and positively charged excitons (trions) on optical absorption of modulation p-doped CdTe-based quantum wells. The density of 2D hole gas in the quantum well was controlled by an additional cw illumination in the range from 1010 cm-2 to 1011 cm-2. Time-resolved absorption was measured following a picosecond, circularly polarized, resonant pump pulse, which created significant exciton population. A spectrally broad femtosecond probe pulse was used to detect the absorption over the excitonic region, including exciton, trion and biexciton transition energies. Besides, we used a small magnetic field (below 1T) to create a steady-state spin polarization of the hole gas. By exploiting polarization-dependent selection rules, we were able to identify exciton, trion and biexciton absorption lines without ambiguity. We studied the evolution of these absorption lines under influence of photo-created populations of excitons and trions. The results are interpreted in terms of spin-dependent exciton-exciton and exciton-carrier interaction, the latter being dominant, in contrast with results obtained on GaAs-based quantum wells. We propose a new explanation of the oscillator strength stealing phenomena observed in doped quantum wells, based on the screening of neutral excitons by charge carriers. We have also found that binding holes into charged excitons excludes them from the interaction with the rest of the system, so that oscillator strength stealing is partially blocked. Experimental evidence is presented for creation of a transient spin polarization in the system by a circularly polarized pump pulse.