C. Hachnasas Lacheder- Bathing and Dressing the child:

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For the occasion of the ceremony, the child is to be bathed and dressed in clean and elegant clothing [i.e. Shabbos clothing].[2]

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[1] Machzor Vitri ibid; Kol Bo ibid; Orchos Chaim 2:3; Meiam Loeiz Parshas Eikev; Shevach Habris 4 p. 139; Nitei Gavriel 18:1

[2] The reason: As this is similar to the giving of the Torah for which the Jewish people bathed themselves and washed their clothing. [Poskim ibid]