New Piginis have glued on treble buttons. There is a video tour of the Pigini factory on Utube and the gluing on operation is shown. I have a 1970's-80's vintage Pigini clone [Artista] that has screw backed buttons, hatched models of which I purchased thru Liberty Bellows in Philly, PA [libertybellows.com]. With glue on buttons, you should be able to see some adhesive "squeeze out" where the button meets the post. It will be obscured by a felt impact pad located between the button and the keyboard that will need to be finessed down toward the backing board. If the felt will not slide down the post, away from the button, you likely have screw on buttons, as the felt bumper gets trapped in between the button and the post during assembly. On glued button assemblies, the felt bumpers are slipped over the posts before the buttons are glued on. Subsequent key action forces the felts up against the button bottom, where it stays from friction.
The screw type buttons are often secured with suprising force. This means that removing them is a scary operation. A screw broken off in the post would be a real bummer, as would be snaping off a glued on example. The tool used will also play a big part. I custom ground an older unused simi-needle nose plier with an inner [in the jaws] radius that approximated the radius of the edge of the buttons. The narrow nose cleared the adjoining buttons and provided a grip that didn't slide off the edge of the button when rotating it. Once you can turn it by finger, depress the "sympathetic" buttons that surround the button being replaced to gain finger clearance and screw it on out.
To reassemble, follow the last sentence in reverse paying attention to engage the screw threads on the button back with the existing threads in the post, that were cut by the original button. Screw as far as possible by finger, then go to the tool. Sight the level of the row of buttons and dial the new button in to level. On my Pig, the hatched portion of the replacement button stood proud of the actual level plane of the row because the thin original buttons matched the "base" thickness of the hatched buttons.
If you're still not sure of what you have, use a dummy button [if your box has them] as a test bed. You can always glue a button back on, especially if it's never used.
Good luck & Press on.../.
Waldo