If they are distant then they are problably outside of your extended family and Geni hides this information because of Data Protection rules (and this is also common sense). Nobody that can help you here, except for you sending a message to managers and asking for the information (but they would probably want to hear a good reason for it).
Kind regards, Hubert
You should be able to see out to 4th cousin and current spouse.
Further distant than that -- you can ask for info as suggested.
You can also ask - via message to managers - to be added as a manager. They would do this by going to the profile and using Actions, then choosing Manager options. You would then have to accept.
Or, if they are within 4th cousin of a geni-user who is within 4th cousin of you that might be willing - ask that geni-user relative to add themself as a manager - you can see and edit all unclaimed profiles managed by someone in your family group.
For example, a third cousin of yours could add themselves as manager of their grandchild, and then you would be able to see its details etc.