The father probably should have told the servants to give the boy a bath, or hose him down or something, before putting him in his best robe.
Btw, no. 38 by Boisselier nicely previews the jealousy. Great collection!
If one accepts the conjecture that the Prodigal represents the Gentiles and the Father stands for God, then yes, a bath is implicit, in the same way that Jesus explained to Peter during footwashing in the upper room: the bath is symbolic of repentant regeneration.