Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
It is lawful to give Zakah to this sister without telling her that it is Zakah provided she is really poor, i.e. a recipient of Zakah.
Otherwise, Zakah should not be given to her as Allah Says (interpretation of meaning): {As-Sadaqât (here it means Zakât) are only for the Fuqarâ' (poor), and Al-Masâkin (the poor) and those employed to collect (the funds); and for to attract the hearts of those who have been inclined (towards Islâm); and to free the captives; and for those in debt; and for Allâh's Cause (i.e. for Mujâhidûn - those fighting in the holy wars), and for the wayfarer (a traveller who is cut off from everything); a duty imposed by Allâh. And Allâh is All-Knower, All-Wise.} [9: 60].
Allah knows best.