My initial thought was that the only reason we bother to read it both ways for parshas zachor is because the reading of zachor is a din d'oraysa, so we want to cover all our bases. For the regular kri'as haTorah of Shabbos which is “only” a din derabbanan, we don't worry if we are off a little bit. If this sevara is correct, then were one were to rely on the MG"A to be yotzei zachor by hearing the kri'ah on Purim morning that comes from the pesukim at the end of Beshalach, then perhaps one should read zeicher/zecher in that context both ways. I've never heard anyone do so.I found a different explanation in the back of the Mahari"l Diskin al haTorah. The Mahari"l quotes the minhag brought in the name of the GR"A (which we will get back to shortly) to read the word in Parshas Ki Teitzei as "zecher" with a segol, and wonders why no one reads it that way here in Beshalach. He suggests that the word "zecher" with a segol has a stronger connotation and implies that men, women, children, and even animals of Amalek must be killed. The word "zeicher," with a tzeirei, has a weaker connotation and does not make that implication clear. In Parshas Ki Teizeti where the Torah is commanding us what to do with Amalek, we spell out clearly the full parameters of the mitzvah, which is to destroy the “zecher” (with a segol) of Amalek, every remnant of them. In Beshalach where the Tora is speaking about what G-d will do to Amalek, "machoh emcheh...," even if the implication is not 100% clear, k'lapei shemaya galya anyway what will happen to them.
A few issues: 1) I don’t know a source for there being a difference in meaning (or at least implication/emphasis) between saying zecher and zeicher (this could just be my own ignorance); 2) In Ma’aseh Rav #28 it is brought down that the GR”A read the pasuk in Ashrei as zecher (with a segol), which suggests that he read ever z-ch-reish word with a segol, including the pasuk at the end of Beshalach; 3) R’ Chaim Volozhiner claimed that he heard the GR”A lein parshas zachor (it is brought down in Ma’aseh Rav that the GR”A would get the aliya and read the parsha himself) and heard the GR”A say zeicher (with a tzeireh). If this is correct, the whole premis behind the Maharil’s observation is moot.Adding up the Ma’aseh Rav, the Mahari”l Diskin, what R’ Chaim Volozhiner reported, it seems that we have different traditions as to what the GR”A said and why he did or didn’t change his reading in different places. How do we make sense of all this? In the footnotes to the new edition of Ma’aseh Rav there is brilliant chiddush suggested by R’ Meshulam Roth that I am going to put together with a GR”A in Kol Eliyahu:
Why was Moshe told specifically in connection with Amalek “sim b’oznei Yehoshua?” Since Moshe had to write the parsha, “..ksov zos zikaron ba’sefer,” wouldn’t that have been enough for Yehoshua to get the message?The GR”A quotes the gemara (Baba Basra 21) that tells us that when David sent Yoav to do battle with Amalek, Yoav killed all the males and reported back, “Mission accomplished.” David was not happy and told Yoav he had only done half the job. He told Yoav she should have killed everyone -- why did do only half the job? Yoav answered that when he was in school, his teacher taught him that the pasuk reads “timcheh es zachar Amalek,” to blot out the males of Amalek, and so he did. What a mistake that teacher made! David corrected Yoav and explained that the pasuk is “timcheh es zeicher Amalek” and everyone must be killed.
Explains the GR”A, this is why the Torah stresses “sim b’oznei Yehoshua,” to, literally translated, “put the [parsha] in Yehoshua’s ear.” Since the Torah has no vowels, without an oral tradition, who knows if the word is zachar (like Yoav misread it) or zeicher? Yehoshua had to hear the words, otherwise he wouldn’t know how to fulfill the mitzvah.Now for the fancy part. When you have a word that has a double kamatz and you put it b’smichut to make a conjunction with another word, the double kamatz changes to a double segol. Take the word “ashan.” If you want to say “smoke of the furnace,” you say “k’eshen hakivshan,” with a double segol, not “k’ashan”. Yoav’s rebbe was not a simpleton who made an obvious error and read “zeicher” as “zachar.” Do you think the rebbe never hear kri’as haTorah or parshas zachor? The mistake was that he heard the ba’al koreh read “zecher” Amalek with a double-segol, instead of “zeicher” with a tzeireh! The rebbe assumed that “zecher Amalek” is b’smichut, and therefore it’s like eshen and ashan, so zecher=zachar, and the mitzvah is to kill only the males.
Based on this, we can explain both mesoros of what the GR”A did, albeit exactly the opposite of how the Mahari”l Diskin thought the GR”A read the parshiyos. When the GR”A read parshas zachor, he read “zeicher” with a tzeireh – not like Yoav’s rebbe’s mistaken reading. This fits with R’ Chaim Volozhiner report of what the GR”A did. However, when the GR”A read the pesukim at the end of Beshalach, where the Torah is reporting, not commanding us what to do, he read it as “zecher,” with a segol.You can nitpick at the loose ends that remain: 1) we still have the Ma’aseh Rav #28 that suggests that the GR”A read everything as zecher and not zeicher; and 2) “Ksov zos zikaron b’sefer v’sim b’oznei Yehoshua” seems to be referring to the parsha of Beshalach, not the pesukim at the end of Ki Teitzeih. Also, based on this there is no reason to reread the word at the end of Ki Teitzeh as “zecher” just to be yotzei the GR”A.
Despite the loose ends, the chiddush gave me a lot of oneg Shabbos. For those reading this, it’s like leftover cholent on Wednesday, but it’s the best I can do.