The rear frame badge may be either polished or painted depending upon your scooter model, but on all series 3 except GP/DL models, the rear badge has a slotted channel along the inside, in to which the frame badge itself is placed.
It can be a bit tricky trying not to scratch the inside of the badge, but with patience, you can bend it by hand and fit it in to the slot. At some point, it will just pop in.
The fitting kit consists of two spacers, two flat washers and two 8mm nuts.
Offer up the completed rear badge and housing to the holes in the rear of the scooter and from the inside, place a spacer, then washer and finally a nut. Finger tighten to check for fit, alignment etc and then finally tighten. Don't go mad with the force. This is a soft alloy and they are easily broken.