This topic comes up pretty frequently, so I’m going to make a post about it that hopefully covers everything in the best ways possible:
Long story short, it’s actually been concluded that —while unusual for the Mediterranean in ancient times— the ancient Hellenes didn’t appear to consider menstruation as a producer of miasma, in and of itself. In fact, there are very few mentions of menstruation at all, outside of medical texts — one of which even suggests sex during menstruation to aid erratic periods (and while this may have nothing to do with irregular periods, many doctors now suggest that sexual intercourse, or at least masturbation during a woman’s period may relieve cramping). In fact, some regions even had a girl’s coming-of-age rites to include sacrificing her first menstrual towels to Artemis.
Now, that said, some women have incredibly painful periods, and that painful cramping, headache, nausea, etc…, may, in fact bring miasma in and of itself, as it’s a physical ailment that has a more concrete effect on the mental / emotional and therefore spiritual self. But the uterus performing its regular function? Apparently not so much. And as others have noted, unwashed hands, on their own, are not miasmic, but disrespectful to approach Ta Theoi with — so I figure women who are experiencing an especially “heavy flow” day but are otherwise fine may not wish to approach the altar or shrine on account of it simply being “less than fresh”, not because of the (apparently false) notion that “menstruation = miasma”.
That aside, ancient Hellas is, as I said, rather unusual for the ancient world, especially the Mediterranean regions, in that there is virtually nothing suggesting that menstruation (and thus all fertile-bodied females, inherently speaking) as being somehow “unclean”, spiritually or otherwise — or at least no more so than any other day-to-day thing that can cause physical uncleanliness.
As for it being “miasma” in that it’s “contact with blood” — well, it’s mostly a mix of placental tissues and and uterine and cervical mucuses, and thus not technically blood — the average menstrual cycle contains maybe a teaspoon of blood from torn capillary veins (as the endometrial tissues slough off); I furthermore have it on good authority from women who’ve actually tasted menstrual fluid as well as actual blood that “blood tastes metallic, menses does not”, so if you have the ability to try it out yourself and wish to test their assurance that “menses ≠ blood”, then by all means, do so — or you can just do what I do, as a non-menstruating human, and take the word of doctors who ought to know these things.
And basically, I’ve had paper-cuts that produced more blood than the average woman’s period. My solution for a paper-cut before ritual? Rinse it in salt-water (my mother was a nurse and says it can actually be helpful, so even pre-polytheism, I’ve always done this), say a prayer to Asklepios, slap a bandage on it, and forget about it. My suggestion for menstruating women? Take a relaxing bath in some bath salts (this can also help relieve cramping) and then change your pad / tampon / cup / towel / whatever before ritual, offer a prayer to Hygaea and Rhea (as menstrual blood seems sacred to Rhea), and forget about it (well, until you need to change your stuff, obviously). The act of menstruation itself is not miasma, the menstrual fluid itself has about as much a taint of “miasma” as a paper-cut — the ancient Hellenes didn’t see menstruation as spiritual uncleanliness, and I see no reason to change this model just because a dozen centuries of Judeo-Christian influence have women running around screaming “UNCLEAN! UNCLEAN!” more-scarier than Diamanda Galas once a month.
If a woman still wishes to abstain from ritual during your period, well, that’s hewr prerogative, I suppose (and I’m just a guy who doesn’t bleed down there, so feel free to not listen to me all you like), but it’s not spiritually necessary in Hellenismos for menstruating women to abstain from anything.