The Greeks believed that any shedding of human blood, including from accidental deaths, made the killer impure, and that they would need to be expiated before they could re-enter civilization. This is typically done by sacrifice, so yes, in a sense, this is a ritual, but one that is common to the Greek experience (as common as accidental homicide is).
To quote the BMCR review of Bernard Eck's book on purification:
**To remove pollution, a purificatory rite or katharmos, was required. Within this rite, Eck considers particularly relevant the act of killing again: the repetition of the phonos was more important than the shedding of blood. [...] [Animal] sacrifice modified the status of the murderer, reintegrating him into his social community. The ritual worked according to the rule of similia similibus curantur: the sacrifice was an authentic expression of magic thought.
That Circe is a witch is incidental. High ranking priests or other representatives of the gods (kings, other community leaders) could also perform a purification rite. (See Robert Parker's book Miasma, p. 135) These rights were simply a part of the ancient Greek religious experience, not something specific to marginal magic-wielders.
As far what actually happened, this is detailed in Apollonius' Argonautica (4.704-717), which is where I presume your sources is getting their information. Therein, we find this expiation passage:
First, to atone for the murder still unexpiated, she held above their heads the young of a sow whose dugs yet swelled from the fruit of the womb, and, severing its neck, sprinkled their hands with the blood; and again she made propitiation with other drink offerings, calling on Zeus the Cleanser, the protector of murder-stained suppliants. And all the defilements in a mass her attendants bore forth from the palace -- the Naiad nymphs who ministered all things to her. And within, Circe, standing by the hearth, kept burning atonement-cakes without wine, praying the while that she might stay from their wrath the terrible Furies, and that Zeus himself might be propitious and gentle to them both, whether with hands stained by the blood of a stranger or, as kinsfolk, by the blood of a kinsman, they should implore his grace.
Notice the blood-sprinkling. This is the symbolic action that removed the "stain" of the original blood (i.e. the murder) and replaces it with acceptable blood (the sacrifice). All of this, as Apollonius says, is to propitiate Zeus' wrath, though in other stories (like Orestes' purification by Iphigenia), it's to propitiate the Erinyes.
