No, it wasn't a necessary thing to do (in addition to the actual circumcision) because the LORD had not commanded Zipporah to do it. The action and her words ("You [Moses] are a bridegroom of blood to me") certainly had a symbolic meaning, though that meaning, however, may or may not have been derived from "an ancient marital relationship formula recalling circumcision as a premarital rite," as T. C. Mitchell suggests.
Before we delve further into the somewhat mysterious nature of the incident which triggered the circumcision and the incident which was a result of the circumcision, I think we do well to consider the situation from Zipporah's point of view as the wife of Moses and the mother of Eliezer (see Exodus 18:4).
Zipporah may have been (likely, she was) loathe to perform the surgery on her son. We do not know his age at this time, but he almost certainly was not a newborn or toddler. As a mother, Zipporah's heart would go out to her son and would quite naturally want to protect her child from unnecessary pain and suffering. She may, however, have been desperate to prevent something far worse than a circumcision. More on that in a moment.
Much like Jacob in Genesis 32:22-30, who had a confrontation with YHWH the night before he was to join his family (more on this, later) whom he had sent on before him in their journey back to Seir, in Edom, to meet with his estranged brother, Esau, Moses had a confrontation with the LORD which frightened both him and his wife. Whereas God merely wrestled with Jacob, God was literally going to put Moses to death. The reason: disobedience, for not circumcising his son earlier, eight days after his birth.
Clearly, God took the rite very seriously, since in Genesis, God had told Abraham
"Any uncircumcised male, who has not been circumcised in the flesh, will be cut off from his people; he has broken my covenant" (Genesis 17:14 NIV).
As God's chosen one to lead His people out of slavery and into the land of promise, Moses needed to set a good example for the people whom he was to lead out of Egypt. A lackadaisical attitude about something so important to God was intolerable. So much so, that God was ready to strike Moses dead, had his wife not intervened and done what must have been distasteful to her. To protect her husband from God, however, she steeled herself and circumcised her son Eliezer.
As for the symbolism of throwing the foreskin of her son at her husband Moses' feet, it could have been related to some ancient ritual. If for some reason, a young Hebrew bridegroom was not circumcised prior to marriage, he would have to undergo the rite in order to be married. As for the words, "You are indeed a bridegroom of blood to me" could make sense in this context, but I think there might be something a bit deeper in the words.
Constable quotes Cassuto and Oosthiezen as follows:
The “bridegroom of blood” figure (v. 26) evidently means as follows. Apparently Zipporah regarded her act of circumcising her son as what removed God’s hand of judgment from Moses and restored him to life and to her again. It was as though God had given Moses a second chance and he had begun life as her husband over as a bridegroom (cf. Jonah). She had accepted Yahweh’s authority and demands and was now viewing Moses in the light of God’s commission. She abandoned her claim to Moses and made him available to Yahweh’s service."
As for the seriousness of Moses' breach of his sacred duty,
“Moses has been chosen and commissioned by God, but he has shown himself far from enthusiastic about confronting the Pharaoh and threatening him with the death of his son. YHWH sets about showing Moses that although he is safe from other men (Ex. iv 19) he faces a much greater danger to his life in the wrath of the God whom he is so reluctant to serve (iv 14). Like Jacob before him, Moses must undergo a night struggle with his mysterious God before he can become a worthy instrument of YHWH and can enjoy a completely satisfactory relationship with his brother. In all this, Moses, like Jacob, is not only an historical person, but also a paradigm. The Israelite people, the people whom YHWH has encountered and whom he will slay with pestilence and sword if they go not out into the wilderness to serve him (v. 3), must ponder this story with fear and trembling.” (Bernard P. Robinson, "Zipporah to the Rescue: A Contextual Study of Exodus IV 24-6" Vetus Testamentum 36:4 (1986): 447-461.)
In summary, then, Zipporah's actions and words could very well be symbolic of having rescued her husband Moses from death, and through her act of obedience she received Moses back from the dead, as it were, for a second chance at marriage. Hence we hear her say,
"You are indeed a bridegroom of blood to me!"
The symbolism of either throwing the foreskin at Moses' feet or touching his feet with it, the versions are about equally divided on this point (although some commentators and Bible versions such as the Common English Bible translate Zipporah's action as touching Moses' genitals with her son's foreskin) was her way of casting the blame at Moses' feet (or genitals, as per the CEB!) for the near-death experience of her husband and the much-too-late circumcision of her son .
Thank God, Zipporah did the right thing, and in doing so saved the life of her husband, though at the relatively minor--though heartbreaking--price of circumcising her son.