Context. To date, stellar activity is one of the main limitations in detecting small exoplanets via the transit photometry technique. Since this activity is enhanced in young stars, traditional filtering algorithms may severely underperform in attempting to detect such exoplanets, with shallow transits often obscured by the photometric modulation of the light curve. Aims. This paper aims to compare the relative performances of four algorithms developed by independent research groups specifically for the filtering of activity in the light curves of young active stars, prior to the search for planetary transit signals: Notch and LOCoR (N&L), Young Stars Detrending (YSD), K2 Systematics Correction (K2SC), and VARLET. Our comparison also includes the two best-performing algorithms implemented in the Wōtan package: Tukey's biweight and Huber spline algorithms. Methods. For this purpose, we performed a series of injection-retrieval tests of planetary transits of different types, from Jupiter down to Earth-sized planets, moving both on circular and eccentric orbits. These experiments were carried out over a set of 100 realistically simulated light curves of both quiet and active solar-like stars (i.e., F and G types) that will be observed by the ESA Planetary Transits and Oscillations of stars (PLATO) space telescope, starting 2026. Results. From the experiments for transit detections, we found that N&L is the best choice in many cases, since it misses the lowest number of transits. However, this algorithm is shown to underperform when the planetary orbital period closely matches the stellar rotation period, especially in the case of small planets for which the biweight and VARLET algorithms work better. Moreover, for light curves with a large number of data-points, the combined results of two algorithms, YSD and Huber spline, yield the highest recovery percentage. Filtering algorithms allow us to obtain a very precise estimate of the orbital period and the mid-transit time of the detected planets, while the planet-to-star radius is underestimated most of the time, especially in cases of grazing transits or eccentric orbits. A refined filtering that takes into account the presence of the planet is thus compulsory for proper planetary characterization analyses.