All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is no contradiction between the scholarly view that it is obligatory or recommended for the Muslim woman to cover her face and the permissibility of trying to see her without her knowledge (if a man is interested in marrying her). The fact that she covers her face does not necessarily entail that there should be no occasion when he may be able to look at her face. She may uncover her face when she is in the company of other women or inside her house or in the company of her Mahram (permanently unmarriageable) men or the like; these are possible scenarios. This happened during the lifetime of the Prophet, sallallaahu ‘alayhi wa sallam, with Jaabir . Jaabir narrated that the Prophet, sallallaahu ‘alayhi wa sallam, said, "If one of you proposes marriage to a woman, then if he can look at her to see that which will encourage him to go ahead and marry her, let him do so." (Jaabir said) "I proposed marriage to a young woman, and I used to hide where I could see her until I saw what encouraged me to go ahead and marry her, so I did so." [Abu Daawood]
Allah knows best.