Are women’s faces allowed to be printed on newspapers (or websites)?
There are differing views in this matter, in general, Charedi newspapers are very stringent on this matter.
The below is only a brief outlook of what seems to be the Rebbe’s view:
See Hishkashrus #582 where it brings three points we find by the Rebbe.
1) After the Rebbetzin Chaya Mushka passed away, they put out an album of her where there was also her picture in black and white. The Nitei Gavriel asked how it is proper to put a picture of the Rebbetzin in the book and at the very least one could be stringent in this matter. The Rebbe answered (in a letter of 11th of Adar 5748) that when one does not know her personally and one does not intend to stare at the picture and also it is not in color there is no problem.
Regarding the final point that the Nitei Gavriel claimed that one should at the very least be stringent in this matter, the Rebbe responded that to be stringent here would cause that one is lacking in fulfillment of the verse, “and one shall place the living to heart” as is seen clearly.
2) The Rebbe instructed to Tzivos Hashem when they made publications intended for non-religious children like “The Moshiach Times” that there should also be a design on the front cover of a girl in addition to of a boy so that girls will know that the publication is also intended for them. Also, the fact that the boys and girl stand separately on the cover will highlight the needs for separation of the genders.
3) The printing of Sefer Hashluchim  albums which have pictures of a whole family seems to be more difficult in fitting with #1, since the pictures are in color, albeit of the entire family wedged in one picture. However, the purpose of this book was for each family to see themselves as part of the Shluchim team and not for others to look at the pictures of other women.
What comes out from the above is that a picture of a woman’s face needs to have a specific and justified reason why it should be publicized. If there is a justified reason to place a woman’s face, it should be done in a Tznius way, for example in black and white and only the face or on the corner of the page and not too big. As mentioned earlier, the Tznius character of a Jewish women is such that she strives to be Pnimah, and naturally wouldn’t want her picture made public.
 It is well known that the Rebbe took interest in these Sefarim.