Originally, Mark planned to reveal his real identity and further tell her all things about Allen to prove his point in order to gain her trust so that he could get access to all her memories and find a way to his home planet.
But, after hearing her story, he realized that it is useless and he changed his plans swiftly. He doesn't see any reason to access her memories now. Without his younger brother's presence at either Ixitus Emperor or his home planet, he has no motivation to visit those places.
Yes, there's an afterthought of taking his revenge against his former superior, the friends who betrayed him, and the mafia gang group that turned his life upside down, but still, they aren't as important as his younger member. Finding him takes priority and now Mark has no idea how to accomplish the task.
As a result, he took the approach of being a close friend to Mark who heard about her, that's all.
