How to remove old pearls?

It depends if the pearls have been glued in or crimped in - obviously glued in pearls will be easy to remove by (carefully) heating the back of the pearl holder in a flame to melt the glue, but ones that are crimped in (as on older Selmers) are more difficult to remove without the pearls being damaged.

If you're relacing worn pearls that have been crimped in (and you don't mind them getting damaged on removal), you can replace them with slightly narrower diameter pearls (narrower in diameter compared to the originals) that fit within the inside diameter of the crimped edge and glue them in place.

Try https://www.windcraft.co.uk/

Click on 'repair materials' and then 'pearls'.

They only offer convex pearls (ie. SBA thumb button) in 16.5mm (which can be turned down and hollowed out to make it concave), but they do convex pearls in 14.8mm (which will be alright to fit in a 15mm holder) and flat pearls in 15.75mm which can be turned down and made concave.

Mother-of-pearl sheet can be bought from some craft shops, and the pearl discs cut using a piercing saw, then turned to make them circular and also made concave.

But always wear a dust mask when working with pearl as the dust is very fine, and if you can use water (in a spray bottle) to keep the dust down during cutting, filing and papering, then do that.