There is nothing wrong if a woman currently having her period kiss the dead of their beloved family member before burial. A woman in her menses is not impure as many people mistakenly believe.
Sheikh Salim `Abdus-Salam Ash-Shaykhi, da`iyah and member of the European Council for Fatwa and Research, states: Yes, it is permissible for a menstruating woman to kiss the dead of their beloved family member before burial because a Muslim woman does not become impure even when menstruating.
Moreover, Wael Shihab, a Shari`ah researcher at Al-Azhar University, adds, As far as I know, there is nothing in the sources of the Shari`ah to indicate that it is prohibited for a woman — during her menses — to kiss the dead of their beloved family member before burial.
Therefore, there is nothing wrong in this. A woman in her menses is not impure; it is a common misunderstanding among many people. It is known that some scholars allowed menstruating women to read the Qur’an — from their memory — and to make dhikr.