Alita didn't have any superpowers; she wasn't that powerful enough to communicate telepathic the way that person just did. And this method on its own scared the hell out of her.
Alita never expected that in this world which lacks spiritual energy, there were hidden tigers like this unknown person. Alita very much wanted to return back to her world but this will be her hiding and if she hides away, this person will still find her.
Alita wasn't willing to let go of this world yet as it has been helping her greatly. Alita pondered for a while and decided to go and take a look. If she is in grave danger, the system was there to help her out.
At the same time, she was also nervous and excited to meet this powerful person.
Alita returned to the hotel where she took a shower first and then sat on the bed while she turned the gems into energy stones. She didn't have much use for the gems on their own as the energy is what she wanted.