Clearly, you can see the connections to women who wear tichels/scarves, sheitels/wigs, hats (hats), etc and still want to put on tefillin in a public space. This stuff can get tricky to accomplish, so what does the halakha have to say about it? Does the tefillah shel rosh have to touch the head?
The Mishnah Brurah (27:16, commenting on Shulchan Arukh 27:4 "Nothing should make a separation (חציצה) between the tefillin and your flesh, whether the tefillin for the hand or the head", and the Rema: "This is specifically about the tefillin, but one does not need to be careful about the straps") considers the question, and gives the following comment:
אין להקפיד - והאחרונים כתבו דאין להקל רק במקום הכריכות אבל מה ששייך להקשירה יש להחמיר אף ברצועות בין בשל יד ובין בשל ראש וכתבו תוכחת מגולה על המניחים התפילין ע"ג פאה נכרית הנקרא פארוק"ה ואפילו אם רק הרצועה מונח על הפאה נכרית. ומ"מ משמע מדברי המ"א והח"א דאם יש לו מכה בראשו ורק במקום שהרצועות מונחים ולא במקום הקציצה מותר לו להניח הרצועות ע"ג סמרטוטין שעל המכה או ע"ג כובע דק ולברך אע"ג שיש חציצה בין הרצועות כיון דבמקום הקציצה אין חציצה וכן בשל יד אם יש לו מכה אפילו במקום הקף הקשר שסביב ידו מותר לו להניח הקף הקשר ע"ג סמרטוטין ולברך אך בזה יזהר לכסות מלמעלה כדי שיתקיים לך לאות
ולא לאחרים לאות:
One does not need to be careful: And the Achronim wrote that one only needs to be careful in the place where they come together. However, since it is pertinent to the knots, one should be stringent also with the straps, both for the tefillin of the hand and of the head. And they wrote a clear rebuke about wearing tefillin over the foreign hair called a perukeh (i.e. a wig), even if only the straps rest on the false hair. And in any case, we learn from the words of the Magen Avraham and the Hayei Adam that if one has a wound on his head and it is only in the place where the straps cross, and not where the tefillin itself sit, it is permissible to wear a rag or a thin hat, and to bless (upon putting on the tefillin), even though there is a separation (חציצה) between the person and the straps, since there is no separation where the tefillin itself sit. Thus too for the tefillin of the hand...
Comment:
This halakha seems to be somewhat self-contradictory: why should it be okay for straps to rest on bandage, but not on a wig? Perhaps it is because the bandage is temporary and prevents pain (and possibly blood getting on your tefillin straps), while the wig is likely on-going but more easily removable. [A historical note: the Mishnah Berurah's author lived from 1839 to 1933, so late for men to be regularly wearing wigs, even when he was young.]
On the one hand, the Shulchan Arukh on its own would seem to open up the wearing of tefillin with the straps over a wig or other covering, as long as one was careful not to let anything come between oneself and the tefillin. However, the Mishnah Berurah is considerably more concerned, and forbids this, even though it cites what sounds like a permissive precedent, namely the case of bandages under the straps being permitted.
The Mishnah Berurah's reasoning is based on concern that the knots of the tefillin straps Do need to touch the person without any separation, which he extends from the knots to the entire volume of the straps.
