Alexa has no idea that Prince Alexander had lost his memory. The only thing on her mind was he's interested in another woman, and he has forgotten about the woman he supposed to love. Her!
She didn't want to make a scene and attracted people around them. Therefore, Alexa stayed quiet, and while they were walking out of the club towards the private elevator. Deep inside her, she's hurting and upset. But she couldn't divulge to him who she is, and she wanted him to discover himself.
Unfortunately, unless Prince Alexander regains his memory once they arrived in the room, that would never happen...
As they walk towards the elevator, Prince Alexander has his arms on her shoulder. While he put Alexa's arms around his waist and locked her in his embrace as they saunter towards their destination.