Still working on that. I think you have to do other missions to trigger her to take it. Someone else posted that If you talk to Lui Kang in the Hotaru village, he will thank you for giving the info on Tanya. Lui Kang will not talk to me unti later (his own words).

My first profile I was able to give it to her. Not the Tanya near the portal you fight, but the one in the same place you get her mission.
My second, I decided to talk to Liu Kang in the big walled city instead, and he said something like "Yes I am Liu Kang" and then gave me 500 something koins. I wasnt able to get Tanya to take the map back, in fact the Tanya I got the mission from wasn't there again.
My conclusion: you can go either of 2 routes, give the map to Tanya, or talk to Liu Kang (assuming Shujinko tells him of her plot) and get stuck with the map in your inventory.
Hope that helps!