If you look at the wording of the prayer, there is nothing more sinister than that about it.
The "Prayers for a Woman on the 40th Day After Childbirth" (the "churching" of the mother before the baptism of her child) make explicit reference to the "uncleanness" of the mother, and so do those that are prescribed for use one day after childbirth.
From
Baptism, Department of Relgious Education, OCA, 1972:
Excerpt from a prayer on page 29: "....Wash away her bodily uncleanness..." At least one other prayer has a similar reference to the "unclean" state of the mother.
From the
Book of Needs [Abridged] St. Tikhon's Seminary Press 2002, pages 3-4:
[Excerpt from the 2nd] Prayer for a Woman on the First Day after Childbirth:
"....Have mercy on her and on the infant, and cleanse her from bodily uncleanness and the various afflictions of her womb..."
[Entire text of the 3rd] Prayer for a Woman on the First Day after Childbirth:
"Let us Pray to the Lord. Lord, have mercy.
O Lord our God, Who was well-pleased to come down from heaven and be born of the Holy Theotokos and Ever-virgin Mary, for the sake of the salvation of us sinners, knowing the frailty of human nature:
According to the multitude of Your compassions, forgive Your servant N., who has given birth today. For You have said, O Lord: "Be fruitful and multiply; fill the earth and subdue it." Therefore, we, your servants, pray, and having boldness on account of your benign love for mankind, with fear we cry out to the Dominion of Your holy Name:
Look down from heaven and behold the feebleness of us who are condemned. Forgive this, your servant, N., and the whole household into which this infant has been born, all who have touched her, and all here present. Forgive all of them, for You are a gracious God and love mankind, and alone have the power to forgive sins, by the prayers of the Most-holy Theotokos and all Your Saints. Amen."
The "Prayers for a Woman on the Fortieth Day After Childbirth" (cited above in the quote from the OCA text
Baptism) contain references to the "bodily uncleanness" of the mother. The quote from the second "Prayer for a Woman on the First Day After Childbirth" shows a clear reference to Jewish law regarding ritual cleanliness. The third prayer is even more clear in its reference, explicitly indicating that a woman who has just given birth and "all who have touched her", or even come near her, are "condemned."! Jewish purity laws are clear in indicating that if one touched someone or something unclean, one would become ritually unclean oneself. I don't see how one can say that there is "nothing sinister" about this kind of language, since it heavily implies that we are still under the sway of the law, an idea that every serious Christian must flatly reject.