Commentary for Exodus 34:34

ודבר אל בני ישראל … וראו AND HE SPOKE UNTO THE CHILDREN OF ISRAEL… AND THEY SAW the rays of glory on his face; and when he moved away from them ...

יסיר את המסוה, whenever Moses had to convey G’d’s instructions to the people he still did not cover his forehead with the cloth he had removed in order to communicate with G’d. Once he concluded conveying G’d’s words he would again cover his forehead. When G’d would address him, or he would wish to address G’d, he did so without wearing the מסוה.

VV. 34 u. 35. Mosche Bescheidenheit ließ es nicht zu, anders als wenn er vor Gott einging oder im Namen Gottes zu reden hatte, sich mit strahlendem Angesicht zu zeigen.

'ובבא משה לפני ה, “whenever Moses went in (the Tabernacle) to face Hashem etc.; either when the communication had been initiated by Hashem, or when Moses had occasion to speak to the people, he did not wear the veil on his face; the reason was, as we learned from Isaiah 30,20: והיו עיניך רואות את מוריך, “your eyes shall be able to see your teacher.” The word: מוריך in that verse refers to G-d Who is your teacher. What G-d was to Moses, Moses was to the people. Just as Moses had not worn a veil when facing G-d and being taught the Torah, so it was not appropriate for him to wear a veil when teaching Torah to the people. When the Torah wrote: והשיב משה את המסוה, “Moses put the veil back on his face,” he did so in order that the people did not have to look at how his forehead emitted the rays of light as it would lose its character of being something holy. Seeing that it was a reflection of the Presence of G-d in miniature, the people were not to relate to it as something that they could feast their eyes on. [Compare Exodus 24 1011 from which it is clear that such an attitude was sinful. Ed.]

The expression מסוה, is based on the word סותה, (compare Genesis 49,11, ובדם ענבים סותה, “his robe in blood of grapes”)