Welcome to the forum. What you termed the “rack” are more correctly called “Chuck Jaws”, although Axminster themselves call them “Accessory Mounting
Jaws” - see picture below. Sadly other manufacturers and even some professional wood turners give them all kinds of names like carriages, carriers and even travellers. The parts that bolt on
top of the Chuck Jaws are often just called jaws or accessory jaws but I prefer the term Top Jaws. This name comes from the metal working industry where the concept of two part Chuck Jaws originally came from. German woodturning tool suppliers can be congratulated for still using this term. Sadly they let themselves down by calling the Chuck Jaws “Base Jaws” but I suppose they can be forgiven for this. It’s not as bad as Travellers!
It’s your choice whether you just remove the Top Jaws or both Chuck and Top Jaws together. If you choose the former buy some spare screws, they are easily lost in shavings!
Although many Wood Turning Chucks have numbers on the body you do not have to worry about which Jaw goes in which slot, the important part is that the Jaws are placed in the chuck body in the
correct order. Including those for my metal lathe I have six or seven chucks and only one has numbers on the Chuck body.
I personally think putting numbers on the body is useful but not all manufacturers do it.