In a deep bowl, mix the gum paste with the flavoring, and water until it forms a very thick paste.
Put parchment paper on a baking sheet, and dust with powdered sugar.
Put the "dough" on the parchment, and dust with a bit more powdered sugar. Press it as thin as you can with the heel of your hand.
Now at this point, you could make little balls, use a tiny mold to make these cute shapes, or even use a fat straw to punch out circles. That is a lot of work, so I recommend dusting a pizza cutter with powdered sugar and cut them into strips and pieces.
Fill a lidded container with the pieces, and sprinkled a bit more powdered sugar in there. Shake it a few times to make sure that all the pieces are coated enough to not stick to each other.
Spread the pieces back on the baking sheet with the parchment, and let dry at room temperature for at least 3 days. Your house will smell awesome, but please watch out for kiddos and pets. If you are using Xylitol it is especially dangerous for pets.
Place finish mints in a mesh strainer and shake to remove the excess powdered sugar. Transfer to lidded containers and/or cute jars for giving as gifts.