Problem

A desk is greyed out

The desk is taken for that day, archived, or it is somebody else's fixed desk.

What you see

In the desk picker a desk cannot be tapped, or it carries the note Booked.

Three reasons are possible:

Somebody has already booked that desk for that day. On any one day a desk belongs to exactly one person.
The desk is somebody else's fixed desk. It is then permanently out of the bookable pool, including on days when nobody is in. That also applies when the person has not registered yet and only sits on your space's list.
Your space has archived the desk.

A fourth case looks similar: in an open area you do not book a desk but a seat. If the area is full, the whole tile cannot be picked.

Take a different desk in the same area.
Try another date. Occupancy applies per day.
If you depend on one particular desk, ask your space. Only they can change a fixed assignment or bring an archived desk back.

Ask your space first. If the app does something wrong: report a problem.