Mishnah Berurah — משנה ברורה

The same applies to Chol Hamoed - The Achronim wrote that since there's an opinion to not wear tefillin at all on Chol Hamoed, as seen below in siman 31, one should quickly remove them before Hallel, and the shaliach tzibur should remove his after Hallel. On Chol Hamoed Sukkos, when there's extra time while they're waiting for an esrog to be brought, even the shaliach tzibur should remove them before Hallel. On Rosh Chodesh, those who wear tefillin all day should put them back on after Mussaf, and they do not need to repeat the blessing if they had in mind to put them back on at the time they removed them, as per the ruling of the Rem"a above in se'if 12. But on Chol Hamoed they should not put them back on at all until the evening. Those who wear Rabbeinu Tam tefillin should not put them on at all on Chol Hamoed, and on Rosh Chodesh they may put them on after the shaliach tzibur finishes Mussaf, or they can remove the Rashi tefillin before "Uva Letzion" and then wear the Rabbeinu Tam while saying "Uva Letzion". [Pri Megadim]