We have studied the times delay of slow electrons scattered by a spherically symmetric rectangular potential well as functions of the well parameters. We have shown that the electron interaction with the scattering center qualitatively depends on the presence of discrete levels in the well. While electron retention dominates for the potential well with no discrete levels, the appearance of a level leads to the opposite situation where the incident electron hardly enters the scatterer. Such a behavior of the time delay is universal since we found it not only for the first s-level but also for the following arising s-, p-, and d-levels.