  We consider the totally asymmetric simple exclusion process on $\Z$ with step
initial condition and with the presence of a rightward-moving wall that
prevents the particles from jumping. This model was first studied in
[Borodin-Bufetov-Ferrari'21]. We extend their work by determining the limiting
distribution of a tagged particle in the case where the wall has influence on
its fluctuations in neighbourhoods of multiple macroscopic times.
