Those who wear tefillin on chol hamoed remove them before beginning Hallel. What is the reasoning behind doing that? Also, is there an ideal time to remove them (e.g., before or after the repetition of the amida).
Very nice and complete answer here from Rabbi Ari N. Enkin
In a nutshell
- The first reason is related to the Mussaf liturgy. According to nusach sefard and sefardi, the Mussaf Kedusha opens with the words “keter yitnu lecha” (“We crown you, our Lord…”) referring to the teaching that the Jewish people, along with the angels, crown God as King of the world. It is explained that it would be unbecoming to make reference to God as the Supreme crowned being while one is wearing tefillin, which are considered to be a crown in their own right.
- The second reason is in order to add a Yom Tov flavor to the day. As Mussaf represents the Yom Tov nature of Rosh Chodesh the tefillin are removed at that time. In fact, some authorities recommend removing the tefillin before the Torah reading as it also represents the Yom Tov nature of the day. There are also those who recommend removing the tefillin before Hallel for the same reason. Some suggest removing the tefillin after the Torah is returned to the aron kodesh. Nevertheless, the halacha is not in accordance with any of these views.