Thruxton Disc Wear

My Doris ( 2011 efi thruxton) has the Honda 3 pot front calliper upgrade, it has the original floating front disc. there is quite a bit of backward and forward movement between the rotor and the disc, could this be wear caused by the superior braking on the buttons(?) rivets(?) between them or natural wear , nearly 20k miles? How would I tell if it’s the buttons that need replacing or the whole part, assuming it’s worth just replacing the buttons( or whatever the feck they’re called)
Cheers