According to Halacha, is it permissible for a Jewish woman who is a Mamzer to donate her eggs to help a non-Mamzer Jewish woman become fertile? Or no, because Mamzerim are prohibited from “entering the congregation of Israel” would it be prohibited? If permissible, would the children be mamzerim or no? One reason why it would matter is because there is a discussion amongst the poskim whether a child from an egg donation can have two halachic mothers (their egg donor and gestational mother).
Let's just go with "Not recommended."
Today, most poskim in both Israel and America will shrug on questions of which mother -- egg or host -- is recognized by halacha, and be strict both ways. (Rabbi Aharon Soloveitchik zt"l forcefully opined that it was the host mother, and only the host mother, but -- today the most common reaction you'll hear from rabbis is "let's play it safe.")
Rabbi Willig has a YUTorah mp3 where he notes that according to Rabbi Moshe Feinstein, mamzer status is conferred upon the next generation only when everything occurs naturally. A mamzer could do IVF and the child would be a non-mamzer. By that logic, then, the donor egg from a mamzeret would not cause the next generation to be mamzerim. Rabbi Willig notes that according to this opinion, you'd have a married couple conceiving all their children through IVF for purely religious, not medical, reasons.
However common practice today is not to rely on that opinion of Rabbi Feinstein.
So while there were some notable opinions (past tense) that this would theoretically not pass on mamzerut, today's poskim would not rely on that. So let's not create any more problems.