Garlic:[1]
Garlic is not Chametz, or Kitniyus, and is thus permitted to be eaten over Pesach.[2] Nevertheless, there are those who are accustomed not to eat garlic on Pesach.[3] Those families who are accustomed to follow this custom are not to swerve from it.[4] However, those families who did not receive such a custom are not required to accept it upon themselves.[5] Nevertheless, if one is part of a community in which everyone is accustomed to be stringent, he is not to be lenient in public regarding this matter.[6]
The Chabad custom: Some[7] record that there is no Chabad custom to avoid eating garlic on Pesach. [Practically, each family is to follow their Minhag.]
______________________________________________
[1] See Sdei Chemed Asifas Diunim Chametz Umtazah 6 Mareches Ayin; Nitei Gavriel 39/5; Otzer Minhagei Chabad p. 63
[2] Chayeh Adam 127/7; Daas Torah 467/2; Zecher Yehosef 120; Madanei Shulchan 117/25; See Beis Yosef 460; Nitei Gavriel ibid
[3] P”M 464 A”A 1 “Some are accustomed not to eat garlic on Pesach”; Chemdas Moshe 22; Pischa Zuta 2/7 that so was custom of Belz [Minhagei Belz p. 41]; Meishiv Halacha 1/309; Otzer Minhagei Chabad Nissan p. 63; Shevach Hamoadim p. 195
The reason: The Poskim state that they do not know the reason behind this custom. [P”M ibid; Rav of Belz stated Otzer ibid] Some however suggest that the reason is because in the times of the Temple people would avoid garlic due to its bad odor which may prevent them from making the pilgramige to the Temple, as rules Rambam Chagiga 2/2. [Dover Meisharim p. 111]
[4] Rav of Belz ibid “Al Titosh Toras Imecha”; However see P”M ibid that one is not to be lenient in this matter in front of an ignoramus although he may be lenient in private in front of Torah scholars.
[5] Bitzel Hachachma 4/113; However see P”M ibid that one is not to be lenient in this matter in front of an ignoramus although he may be lenient in private in front of Torah scholars.
[6] See P”M ibid
[7] Hiskashrus 922 in name of Rav Yaakov Landa; Rav Eli Landa wrote to me in a correspondence that while his father did use garlic during Pesach in Eretz Yisrael, in Russia they did not eat it.
I have hear it said by Rabbi Nissan Dovid Dubov that the reason for this chumra was related to the fact that the goyim had the practice of drying the garlic over an oven that was possibly used to bake chometz.